## Calculus 8th Edition

Need to verify the differential equation: $t\dfrac{dy}{dt}=y+t^2 \sin t$ $t[-\cos t+ t \sin t-1] =[-t \cos t- t]+t^2 \sin t$ or, $- t \cos t +t^2 \sin t-t=-t \cos t- t+t^2 \sin t$ or, $-t \cos t- t=-t \cos t- t$ Now check the initial conditions. Since, we have $y=-t \cos t- t$ when $t =\pi$ Then $y(\pi )=-\pi \cos \pi-\pi$ or, $0=0$ Hence, it has been verified .