Question

y'' + y = 4 x sinx

Answer 1

first you need to find homogenous solution

Answer 2

\[y'' + y =0 \]
\[m^2+1=0\rightarrow m^2=-1\rightarrow m=\pm i\]
\[y=C _{1}cosx+C _{2}sinx\]

Answer 3

for reference
http://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx

Answer 4

i needed particular integral answer. If any one nows the answer please post it . I have to prepare for my internals examination. Plssssssss

Answer 5

you must use integration by parts:
\[\int\limits_{}^{}udv = uv - \int\limits_{}^{}vdu\]
where u=x , and v=sinx
ps. \[\int\limits_{}^{}4xsinx = 4 \int\limits_{}^{}xsinx\]
I hope i was helpful