What is the solution for t((dx)/(dt))+3x=5t^2 ?

The solution for t((dx)/(dt))+3x=5t^2 is x=t^2+(c_{1})/(t^3)

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t((dx)/(dt))+3x=5t^2

t (\frac{d x}{d t}) + 3 x = 5 t^{2}

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

Solution steps

t (\frac{d x}{d t}) + 3 x = 5 t^{2}

Solve linear ODE:

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

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

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

\frac{d}{d x} (12 x^{3} + 12 x^{2})

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

x \to 0 lim (x cos (\frac{11}{2} x))

n \to \infty lim (\frac{1}{n})

What is the solution for t((dx)/(dt))+3x=5t^2 ?
The solution for t((dx)/(dt))+3x=5t^2 is x=t^2+(c_{1})/(t^3)