# Find the solution of the IVP when: {eq}y' = y^2 {/eq}, and {eq}y(1)=1 {/eq}

## Question:

Find the solution of the IVP when: {eq}y' = y^2 {/eq}, and {eq}y(1)=1 {/eq}

## Variable Separable Differential Equation:

A differential equation of the form {eq}f(x) dx = g(x) dy {/eq}, that is called variable separable differential equation.

We have to understand the following steps to solve the differential equation using the variable separable method:

Step 1: Take every x term one side and y term another side

Step 2: Take integration both sides

Step 3: Solve the integration

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Given:

{eq}\displaystyle y' = y^2, \ \ y(1) = 1 {/eq}

We will solve step by step.

\begin{align*} \displaystyle \frac{dy}{dx} &= y^2...