Solution of Ex:4.1 Differential Equations with Boundary-Value Problems (7th Edition Book) consist of initial and boundary value problems. In this post, we will provide solved questions of Ex:4.1 in hard form given below.

### Solution of Ex:4.1 Differential Equations with Boundary-Value Problems (7th Edition Book)

**Exercise**

We first find the GS (general Solution) to the (DE) differential equation y” + y = 0.

The general solution is

where c1 and c2 are constants that depend on the boundary conditions.

Boundary conditions (BCs) are y(0) = 0 and y(pi/2) = 1

Substituting x = 0 , we get

Substituting , we get

Therefore, the solution to the BVP is We can check that this solution satisfies the differential equation and the boundary conditions.

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