q1 solve the following second order differential

Question

Q.1 Solve the following second order differential equations:

              (a) xy' = 2y' ;                   (b) y" + e^2yy'³ =0.

Q.2  Solve the following differential equation:

                     y" + 10y' + 25y =0.

Q.3. Solve the following initial value problem.

             2y' + y' - y = 0, y(4) = e² - e^-4 =7.371,  y'(4) = 1/2e² + e^-4 = 3.713.

Q.4.  Solve the following boundary value problem:

             y" - 2y' = 0, y(0) = -1, y(1/2) = e-2

Q.5 Find a general solution of the following differential equation:

                   y" + 6y' + 9y = 18cos3x.

Q.6. Find a general solution of the following  nonhomogeneous Euler-Cauchy equation:

                   x²y" - 4xy' + 6y = 42/x⁴.