Given the Differential Equation with the Given Initial Condition $\frac { d y } { d t } = y ^ { 2 } \ln t ; \quad y ( 1 ) = \frac { 1 } { 3 }$

True/False

Given the differential equation with the given initial condition: $\frac { d y } { d t } = y ^ { 2 } \ln t ; \quad y ( 1 ) = \frac { 1 } { 3 }$ is this the solution $y = \frac { 1 } { 2 - t \ln t + t } ?$