Consider f(t) = -(2t + 3) sin( t )+ 5 cos(t)
find constants C1, C2, C3 so that the derivative of g(t) = (C1t + C2) cos(t), + C3 sin(t) is equal to f(t)
Did you differentiate $\displaystyle (C_1t+ C_2)\cos(t)+ C_3\sin(t)$? The derivative of $\displaystyle C_1t+ C_2$ is $\displaystyle C_1$, the derivative of $\displaystyle \cos(t)$ is $\displaystyle -\sin(t)$, and the derivative of $\displaystyle \sin(t)$ is $\displaystyle cos(t)$. Of course you will need to use the "product rule" to differentiate $\displaystyle (C_1t+ C_2)\cos(t)$.