# Find the solution of the differential equation that satisfies the given initial condition. {dy} /...

## Question:

Find the solution of the differential equation that satisfies the given initial condition.

{eq}\displaystyle \dfrac {dy} {dx} = \dfrac {x \sin x} {y},\ y (0) = -1 {/eq}

## Separable Differential Equations:

Differential equations come in many different forms, whenever we can separate a differential equation so that only one of the variables appears on either side of the equals sign, we call it separable. We can solve a separable differential equation by first separating the variables, and then integrating both sides. This gives us a general solution, in order to find a particular solution we must have an initial condition.