Modeling by Solving Separable Differential Equations - AP Calculus BC

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Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

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To solve the separable differential equation, we must separate x and y, dx and dy respectively to opposite sides:

Integrating both sides, we get

$\ln\left | y\right |=\frac{ $x^3$}{3}$+C$

The rules of integration used were

$\int $\frac{dx}{x}$=\ln\left| x\right|+C$ , $\int $x^ndx$= $$\frac{x^{n+1}$$}{n+1}+C$

The constants of integration merged into one.

Now, we exponentiate both sides of the equation to solve for y, and use the properties of exponents to simplify:

To solve for C, we use our given condition:

Our final answer is

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Tap to see back →

To solve the separable differential equation, we must separate x and y, dx and dy respectively to opposite sides:

Integrating both sides, we get

$\ln\left | y\right |=\frac{ $x^3$}{3}$+C$

The rules of integration used were

$\int $\frac{dx}{x}$=\ln\left| x\right|+C$ , $\int $x^ndx$= $$\frac{x^{n+1}$$}{n+1}+C$

The constants of integration merged into one.

Now, we exponentiate both sides of the equation to solve for y, and use the properties of exponents to simplify:

To solve for C, we use our given condition:

Our final answer is

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Tap to see back →

To solve the separable differential equation, we must separate x and y, dx and dy respectively to opposite sides:

Integrating both sides, we get

$\ln\left | y\right |=\frac{ $x^3$}{3}$+C$

The rules of integration used were

$\int $\frac{dx}{x}$=\ln\left| x\right|+C$ , $\int $x^ndx$= $$\frac{x^{n+1}$$}{n+1}+C$

The constants of integration merged into one.

Now, we exponentiate both sides of the equation to solve for y, and use the properties of exponents to simplify:

To solve for C, we use our given condition:

Our final answer is

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Tap to see back →

To solve the separable differential equation, we must separate x and y, dx and dy respectively to opposite sides:

Integrating both sides, we get

$\ln\left | y\right |=\frac{ $x^3$}{3}$+C$

The rules of integration used were

$\int $\frac{dx}{x}$=\ln\left| x\right|+C$ , $\int $x^ndx$= $$\frac{x^{n+1}$$}{n+1}+C$

The constants of integration merged into one.

Now, we exponentiate both sides of the equation to solve for y, and use the properties of exponents to simplify:

To solve for C, we use our given condition:

Our final answer is

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Tap to see back →

To solve the separable differential equation, we must separate x and y, dx and dy respectively to opposite sides:

Integrating both sides, we get

$\ln\left | y\right |=\frac{ $x^3$}{3}$+C$

The rules of integration used were

$\int $\frac{dx}{x}$=\ln\left| x\right|+C$ , $\int $x^ndx$= $$\frac{x^{n+1}$$}{n+1}+C$

The constants of integration merged into one.

Now, we exponentiate both sides of the equation to solve for y, and use the properties of exponents to simplify:

To solve for C, we use our given condition:

Our final answer is

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Tap to see back →

To solve the separable differential equation, we must separate x and y, dx and dy respectively to opposite sides:

Integrating both sides, we get

$\ln\left | y\right |=\frac{ $x^3$}{3}$+C$

The rules of integration used were

$\int $\frac{dx}{x}$=\ln\left| x\right|+C$ , $\int $x^ndx$= $$\frac{x^{n+1}$$}{n+1}+C$

The constants of integration merged into one.

Now, we exponentiate both sides of the equation to solve for y, and use the properties of exponents to simplify:

To solve for C, we use our given condition:

Our final answer is

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Tap to see back →

To solve the separable differential equation, we must separate x and y, dx and dy respectively to opposite sides:

Integrating both sides, we get

$\ln\left | y\right |=\frac{ $x^3$}{3}$+C$

The rules of integration used were

$\int $\frac{dx}{x}$=\ln\left| x\right|+C$ , $\int $x^ndx$= $$\frac{x^{n+1}$$}{n+1}+C$

The constants of integration merged into one.

Now, we exponentiate both sides of the equation to solve for y, and use the properties of exponents to simplify:

To solve for C, we use our given condition:

Our final answer is

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Tap to see back →

To solve the separable differential equation, we must separate x and y, dx and dy respectively to opposite sides:

Integrating both sides, we get

$\ln\left | y\right |=\frac{ $x^3$}{3}$+C$

The rules of integration used were

$\int $\frac{dx}{x}$=\ln\left| x\right|+C$ , $\int $x^ndx$= $$\frac{x^{n+1}$$}{n+1}+C$

The constants of integration merged into one.

Now, we exponentiate both sides of the equation to solve for y, and use the properties of exponents to simplify:

To solve for C, we use our given condition:

Our final answer is

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Tap to see back →

To solve the separable differential equation, we must separate x and y, dx and dy respectively to opposite sides:

Integrating both sides, we get

$\ln\left | y\right |=\frac{ $x^3$}{3}$+C$

The rules of integration used were

$\int $\frac{dx}{x}$=\ln\left| x\right|+C$ , $\int $x^ndx$= $$\frac{x^{n+1}$$}{n+1}+C$

The constants of integration merged into one.

Now, we exponentiate both sides of the equation to solve for y, and use the properties of exponents to simplify:

To solve for C, we use our given condition:

Our final answer is

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Tap to see back →

To solve the separable differential equation, we must separate x and y, dx and dy respectively to opposite sides:

Integrating both sides, we get

$\ln\left | y\right |=\frac{ $x^3$}{3}$+C$

The rules of integration used were

$\int $\frac{dx}{x}$=\ln\left| x\right|+C$ , $\int $x^ndx$= $$\frac{x^{n+1}$$}{n+1}+C$

The constants of integration merged into one.

Now, we exponentiate both sides of the equation to solve for y, and use the properties of exponents to simplify:

To solve for C, we use our given condition:

Our final answer is

Modeling by Solving Separable Differential Equations - AP Calculus BC

Solve the separable differential equation with the condition .

Solve the separable differential equation with the condition .

Solve the separable differential equation with the condition .

Solve the separable differential equation with the condition .

Solve the separable differential equation with the condition .

Solve the separable differential equation with the condition .

Solve the separable differential equation with the condition .

Solve the separable differential equation with the condition .

Solve the separable differential equation with the condition .

Solve the separable differential equation with the condition .

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .

Solve the separable differential equation

$\frac{\mathrm{d}$ y}{\mathrm{d} x}= $yx^2$

with the condition .