The solution of the differential equation d2y dx2=sin3x+ex+x2 when y1(0)=1 and y(0)=0 is

Given that d2y dx2=sin3x+ex+x2 Integrating on both sides dydx=−cos 3x3+ex+x33+c And given y1(0)=1⇒1=−13+1+0+C⇒C=−13∴dydx=−cos 3x3+ex+x33Again Integrating on both sidesy=−sin3x9+ex+x412−x3+KAnd given  y (0) = 0⇒0=0+1+0−0+K∴K=−1∴y=−sin3x9+ex+x412−x3−1