Solve the homogenous equation

Find the solutions for the following problems

1) m y"(x) + k y(x) = f sin (Ï?t) subjected to y(0)=0 and y'(0) = 1 , [Ï? not equal to the square root of (k/m)] . m and k are constants .

2) x y"(x) - y'(x) + (1/x) y(x) = 0 subject to y(1) = 0 and y"(1) = 1 .

How is the solution affected if the constraints are changed to y(0) = 0 and y'(0) = 1 ? What is the special about this case?

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How is the solution affected if the constraints are changed : How is the solution affected if the constraints are changed to y(0) = 0 and y'(0) = 1 ? What is the special about this case? |

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