What is the solution for (dy)/(dt)=(6t^5)/(1+t^6)y+7(1+t^6)^2 ?

The solution for (dy)/(dt)=(6t^5)/(1+t^6)y+7(1+t^6)^2 is y=t^{13}+8t^7+c_{1}t^6+7t+c_{1}

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(dy)/(dt)=(6t^5)/(1+t^6)y+7(1+t^6)^2

\frac{d y}{d t} = \frac{6 t ^{5}}{1 + t ^{6}} y + 7 (1 + t^{6})^{2}

y = t^{13} + 8 t^{7} + c_{1} t^{6} + 7 t + c_{1}

Solution steps

\frac{d y}{d t} = \frac{6 t ^{5}}{1 + t ^{6}} y + 7 (1 + t^{6})^{2}

Solve linear ODE:

y = t^{13} + 8 t^{7} + c_{1} t^{6} + 7 t + c_{1}

y = t^{13} + 8 t^{7} + c_{1} t^{6} + 7 t + c_{1}

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What is the solution for (dy)/(dt)=(6t^5)/(1+t^6)y+7(1+t^6)^2 ?
The solution for (dy)/(dt)=(6t^5)/(1+t^6)y+7(1+t^6)^2 is y=t^{13}+8t^7+c_{1}t^6+7t+c_{1}