What is the solution for 12(t+1)(dy)/(dt)-9y=27t ?

The solution for 12(t+1)(dy)/(dt)-9y=27t is y=3(3t+4)+c_{1}(t+1)^{3/4}

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12(t+1)(dy)/(dt)-9y=27t

12 (t + 1) \frac{d y}{d t} - 9 y = 27 t

y = 3 (3 t + 4) + c_{1} (t + 1)^{\frac{3}{4}}

Solution steps

12 (t + 1) \frac{d y}{d t} - 9 y = 27 t

Solve linear ODE:

y = 3 (3 t + 4) + c_{1} (t + 1)^{\frac{3}{4}}

y = 3 (3 t + 4) + c_{1} (t + 1)^{\frac{3}{4}}

cos (4) x^{3}

\frac{d}{d x} (4 x y^{2} - x y^{3} - x^{2} y^{2})

cot^{2} (π x)

8 (2 z e^{z} + e^{z} z^{2})

\frac{d y}{d x} = - 4 x y^{2}

What is the solution for 12(t+1)(dy)/(dt)-9y=27t ?
The solution for 12(t+1)(dy)/(dt)-9y=27t is y=3(3t+4)+c_{1}(t+1)^{3/4}