What is the solution for (dx)/(dt)+4tx=t,x(0)=0 ?

The solution for (dx)/(dt)+4tx=t,x(0)=0 is x= 1/4-1/(4e^{2t^2)}

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(dx)/(dt)+4tx=t,x(0)=0

\frac{d x}{d t} + 4 t x = t, x (0) = 0

x = \frac{1}{4} - \frac{1}{4 e ^{2 t^{2}}}

Solution steps

\frac{d x}{d t} + 4 t x = t

Solve linear ODE:

x = \frac{1}{4} - \frac{1}{4 e ^{2 t^{2}}}

x = \frac{1}{4} - \frac{1}{4 e ^{2 t^{2}}}

\int \frac{x}{7} 49 + x^{2} d x

\frac{d}{d x} (e^{- 2 x} - x)

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\frac{\partial}{\partial y} (y^{3} cos (4 x))

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

What is the solution for (dx)/(dt)+4tx=t,x(0)=0 ?
The solution for (dx)/(dt)+4tx=t,x(0)=0 is x= 1/4-1/(4e^{2t^2)}