Given the Differential Equation with the Given Initial Condition $\mathrm { y } ^ { \prime } = \mathrm { t } \cos \mathrm { t } ; \mathrm { y } ( 0 ) = 0$

True/False

Given the differential equation with the given initial condition: $\mathrm { y } ^ { \prime } = \mathrm { t } \cos \mathrm { t } ; \mathrm { y } ( 0 ) = 0$ is this the solution $y = t \sin t + \cos t - 1 ?$