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}

y^{^{'}} = x^{2} sec (y)

\int_{0}^{1} x e^{- 3 x^{2}} d x

n = 0 \sum \infty arctan (2 n)

(2, 2), (0, - 1)

x \to 0 - lim (\frac{5}{sin ( x )})

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)