Additional Problems On Differential Equations

Problems:

3. Solve

Solutions: We have (D² a²) y = tan ax

                A.E is m² a² = 0 ⇒ m = ± ia

               C.F is = C₁ cos ax C₂ sin ax

be the complete solution of the d.e. Where A and B are function of x to be found.

Substitute these value in the above equation we get;

5. Using the method of variation of parameter find the solutions

Solutions: we have (D² 2D 1) y = e^x/x

                A.E is m² - 2m 1 = 0 ⇒ (m-1)² = 0

              ∴ m = 1,1 are the root of A.E

Where A = A(x), B = B(x)

be the complete solutions of the d.e and we shall find A,B we have;