What is the solution for (dy)/(dt)-(4t)/(1+4t^2)y=4t ?

The solution for (dy)/(dt)-(4t)/(1+4t^2)y=4t is y=1+4t^2+c_{1}sqrt(1+4t^2)

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(dy)/(dt)-(4t)/(1+4t^2)y=4t

\frac{d y}{d t} - \frac{4 t}{1 + 4 t ^{2}} y = 4 t

y = 1 + 4 t^{2} + c_{1} 1 + 4 t^{2}

Solution steps

\frac{d y}{d t} - \frac{4 t}{1 + 4 t ^{2}} y = 4 t

Solve linear ODE:

y = 1 + 4 t^{2} + c_{1} 1 + 4 t^{2}

y = 1 + 4 t^{2} + c_{1} 1 + 4 t^{2}

\frac{\partial}{\partial x} (1000)

f (x) = 4 e^{4 x}

\int 2 (1 - cos (x)) d x

\int \frac{1}{4 x - 1} d x

2 y^{^{''}} - 8 y = 0, y (- 2) = 2, y^{^{'}} (- 2) = 1

What is the solution for (dy)/(dt)-(4t)/(1+4t^2)y=4t ?
The solution for (dy)/(dt)-(4t)/(1+4t^2)y=4t is y=1+4t^2+c_{1}sqrt(1+4t^2)