# Solve the IVP: {eq}\displaystyle \frac{dy}{dx}=5xy\ sin(3x^2), \ y(0)=1 {/eq}

## Question:

Solve the IVP:

{eq}\displaystyle \frac{dy}{dx}=5xy\ sin(3x^2), \ y(0)=1 {/eq}

## Differential Function with Trig-function:

For the simplification of the integration of the given trig-function, we'll use the substitution method of the integrals. For that, we need to change the variable {eq}x {/eq} as the variable {eq}u {/eq} or {eq}t {/eq} by substituting and differentiating the terms.

After that, we'll compute the value of constant of integration {eq}(C) {/eq} using the given initial condition for the proper solution of the given differential equation.

## Answer and Explanation: 1

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The given differential equation with trig-function is:

{eq}\displaystyle \frac{dy}{dx}=5xy\ sin(3x^2) \\ y(0)=1 {/eq}

Separating like variables on...

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