What is the solution for (dy}{dt}=-\frac{3y)/t-2-t^{-4},y(1)=4 ?

The solution for (dy}{dt}=-\frac{3y)/t-2-t^{-4},y(1)=4 is y=-t/2-(ln(t))/(t^3)+9/(2t^3)

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(dy}{dt}=-\frac{3y)/t-2-t^{-4},y(1)=4

\frac{d y}{d t} = - \frac{3 y}{t} - 2 - t^{- 4}, y (1) = 4

y = - \frac{t}{2} - \frac{ln ( t )}{t ^{3}} + \frac{9}{2 t ^{3}}

Solution steps

\frac{d y}{d t} = - \frac{3 y}{t} - 2 - t^{- 4}

Solve linear ODE:

y = - \frac{t}{2} - \frac{ln ( t )}{t ^{3}} + \frac{9}{2 t ^{3}}

y = - \frac{t}{2} - \frac{ln ( t )}{t ^{3}} + \frac{9}{2 t ^{3}}

What is the solution for (dy}{dt}=-\frac{3y)/t-2-t^{-4},y(1)=4 ?
The solution for (dy}{dt}=-\frac{3y)/t-2-t^{-4},y(1)=4 is y=-t/2-(ln(t))/(t^3)+9/(2t^3)