What is the solution for t^3(dx)/(dt)+3t^2x=t ?

The solution for t^3(dx)/(dt)+3t^2x=t is x= 1/(2t)+(c_{1})/(t^3)

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t^3(dx)/(dt)+3t^2x=t

t^{3} \frac{d x}{d t} + 3 t^{2} x = t

x = \frac{1}{2 t} + \frac{c _{1}}{t ^{3}}

Solution steps

t^{3} \frac{d x}{d t} + 3 t^{2} x = t

Solve linear ODE:

x = \frac{1}{2 t} + \frac{c _{1}}{t ^{3}}

x = \frac{1}{2 t} + \frac{c _{1}}{t ^{3}}

t an g e n t y = x^{2} e^{- x}, (1, \frac{1}{e})

\frac{d}{d x} (3^{x})

\int_{0}^{1} \frac{5}{x ^{2} + 1} d x

\int (\frac{3}{x} + 2 e^{x}) d x

a re a x^{2}, 12 - x, [- 3, 4]

What is the solution for t^3(dx)/(dt)+3t^2x=t ?
The solution for t^3(dx)/(dt)+3t^2x=t is x= 1/(2t)+(c_{1})/(t^3)