Question

Q:7 Find the particular solution of each of the following equations by the method of undetermined coefficients and hence find its general solution.

1) y" + 4y = 2 cos ^x + 10 e ^x
2) y" + y = sin x + (1 + x ^2) e^x
3) y"-y = e^(-x) (sin x + cos x)
4) y"'-3y"-y'+3y = x^2 e ^x


Q:8 By using the method of parameters , find the general solution of :

1) y" + 4y = 2cos^x + 10e^x
2) y" + y = x sin x
3 )y" + y = cot ^2 x
4) x^2 y" -x(x+2)y' + (x +2) y = x ^3
where x >0 .


For Better Clarity see Pic attached to it.

Answer 1

1) Method of Undetermined Coefficients
2) Method of variation of parameters.



Here, due to lack of space I provided the solution of Fourth parts (typical one) of both the questions.