For the ODE: u +4u = f(x),0 < x...

 

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For the ODE: u" +4u = f(x),0 < x <^ u(0) = 0,u(z) = 0 And let the operator be L(u)=u'+4u, with u(0) = u(x) = 0. a) Compute the adjoint operator of L. b) Compute Ker(L) and Im(L). c) For f(x)=a+bx, find the condition for a and b, so that the ODE has the solution and find its solution. d) For f(x) = ax + b sin(2x), find the condition a and b, so that the ODE has the solution and find its solution. For the ODE: u" +4u = f(x),0 < x <^ u(0) = 0,u(z) = 0 And let the operator be L(u)=u'+4u, with u(0) = u(x) = 0. a) Compute the adjoint operator of L. b) Compute Ker(L) and Im(L). c) For f(x)=a+bx, find the condition for a and b, so that the ODE has the solution and find its solution. d) For f(x) = ax + b sin(2x), find the condition a and b, so that the ODE has the solution and find its solution.