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)
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.