Given the Differential Equation with the Given Initial Condition $y y ^ { \prime } = \operatorname { te } ^ { \mathrm { t } ^ { 2 } } ; \quad y ( 0 ) = 1$

True/False

Given the differential equation with the given initial condition: $y y ^ { \prime } = \operatorname { te } ^ { \mathrm { t } ^ { 2 } } ; \quad y ( 0 ) = 1$ is this the solution $y = e ^ { t ^ { 2 } / 2 } ?$