Homogeneous solution:
\(\displaystyle \L\\2y'(x)+y''(x)=x\)
\(\displaystyle \L\\r^{2}+2r=0\)
\(\displaystyle \L\\r(r+2)=0\)
\(\displaystyle \L\\r_{1}=0\)
\(\displaystyle \L\\r_{2}=-2\)
\(\displaystyle \L\\y_{H}=C_{1}+C_{2}e^{-2x}\)
How do I find particular solution?
\(\displaystyle \L\\2y'(x)+y''(x)=x\)
\(\displaystyle \L\\r^{2}+2r=0\)
\(\displaystyle \L\\r(r+2)=0\)
\(\displaystyle \L\\r_{1}=0\)
\(\displaystyle \L\\r_{2}=-2\)
\(\displaystyle \L\\y_{H}=C_{1}+C_{2}e^{-2x}\)
How do I find particular solution?