Problems On Method Of Undetermined Coefficients

Problems on Method of Undetermined Coefficients-1:

5. Solve by the method of undetermined coefficient y'' 4y = x² e^-x

Solution: We have (D² 4)y = x² e^-x

               A.E is m² 4 = 0

              m² = -4

             m = ±2i

Where 0 and -1 is not root of the A.E, We assume for P.I in the form;

We have to find a, b, c, d such that;

Equating the coefficients;

So the general solution is y = C.F P.I

6. Solve the method of undetermined coefficients y'' y' - 4y = x cos 2x

Solution: We have (D² - D - 4)y = x cos 2x

              A. E is m² - m - 4 = 0

On solving the above equation we get;