What is the solution for 12(t+1)((dy)/(dt))-8y=32t,y(0)=2 ?

The solution for 12(t+1)((dy)/(dt))-8y=32t,y(0)=2 is y=4(2t+3)-10(t+1)^{2/3}

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12(t+1)((dy)/(dt))-8y=32t,y(0)=2

12 (t + 1) (\frac{d y}{d t}) - 8 y = 32 t, y (0) = 2

y = 4 (2 t + 3) - 10 (t + 1)^{\frac{2}{3}}

Solution steps

12 (t + 1) (\frac{d y}{d t}) - 8 y = 32 t

Solve linear ODE:

y = 4 (2 t + 3) - 10 (t + 1)^{\frac{2}{3}}

y = 4 (2 t + 3) - 10 (t + 1)^{\frac{2}{3}}

y = \frac{1}{t ^{3} + 2 t ^{2} - 1}

x = - 5, x = 1, y = 3 x, y = x^{2} - 4

\frac{d}{d x} (\frac{4 x - 7}{2 x + 1})

\int \frac{6 x ^{2} - 5 x + 3}{x} d x

\frac{\partial}{\partial x} (3 x y e^{y - x})

What is the solution for 12(t+1)((dy)/(dt))-8y=32t,y(0)=2 ?
The solution for 12(t+1)((dy)/(dt))-8y=32t,y(0)=2 is y=4(2t+3)-10(t+1)^{2/3}