# Solve the IVP: {eq}\displaystyle y' = \sin^2 (x - y),\ y\bigg(\dfrac \pi 2\bigg) = \dfrac \pi 4 {/eq}

## Question:

Solve the IVP:

{eq}\displaystyle y' = \sin^2 (x - y),\ y\bigg(\dfrac \pi 2\bigg) = \dfrac \pi 4 {/eq}

## Initial Value Problem

A differential equation is an equation which tells relations between the functions along with their derivative.

Initial value problems are ordinary differential equation along with the initial condition which when applied to the solution of the differential equation , provides the value of unknown function in a domain.

To solve the initial problem, first solve the differential equation and then substitute the initial condition into the solution to find the value of unknown function {eq}C {/eq}.

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Rewrite the given problem,

{eq}\dfrac{dy}{dx}={{\sin }^{2}}\left( x-y \right),y\left( \dfrac{\pi }{2} \right)=\dfrac{\pi }{4} {/eq}

Let...