**Example:** Solve the initial value problem

**Answer:** This is a separable equation. Indeed, we have

Before we get into integration we need to look for the constant solutions. These are the roots of the equation . Since this equation has no real roots, we conclude that no-constant solution exists. Therefore, we proceed with the separation of the two variables and integration. We have

,

which gives

Since

and

,

we get

The initial condition *y*(0)=1 gives

The particular solution to the initial value problem is

,

or in the explicit form

**
**

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Contact us

Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA

users online during the last hour