Method of undetermined coefficients

[sky_tm]

\[\frac{{d^2 y}}{{dx^2 }} - \frac{{dy}}{{dx}} + 6y = 36x + 50\sin x\]
find particular solution of the differential equation which satisfies the
initial conditions
\[y = 0,\frac{{dy}}{{dx}} = 0,x = 0\]

 

[v_c]

I am attaching the solution in the pdf file. I used the open source tool called Maxima
( http://maxima.sourceforge.net/ ) to do the analysis. The blue lines are the inputs and the black lines are the outputs. The first blue line solves the differential equation and since it is a second order differential equation two unknown constants (%k1 and %k2) appear in the first black line. The second blue line applies the initial conditions to the solution and the results appear right after that.

Hope this helps you out.

Best regards,
v_c[/img]