Given the differential equation: $y ^ { \prime } = 3 t ^ { 2 } ( y - 7 )$ , is this the solution $y = 7 + \mathrm { ce } ^ { t ^ { 3 } } ?$

Question

Quizplus · Accepted Answer

To verify if $y = 7 + ce^{t^3}$ is a solution, we differentiate it with respect to $t$ to get $y' = 3t^2ce^{t^3}$. Substituting $y$ and $y'$ into the given differential equation, we find that it satisfies the equation, confirming it as a solution.

Given the Differential Equation y′=3t2(y−7)y ^ { \prime } = 3 t ^ { 2 } ( y - 7 )y′=3t2(y−7)

Given the Differential Equation $y ^ { \prime } = 3 t ^ { 2 } ( y - 7 )$