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

The solution for (dx)/(dt)x=t^2-5 is x=sqrt((2t^3)/3-10t+c_{1)},x=-sqrt((2t^3)/3-10t+c_{1)}

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(dx)/(dt)x=t^2-5

\frac{d x}{d t} x = t^{2} - 5

x = \frac{2 t ^{3}}{3} - 10 t + c_{1}, x = - \frac{2 t ^{3}}{3} - 10 t + c_{1}

Solution steps

\frac{d x}{d t} x = t^{2} - 5

Solve separable ODE:

x = \frac{2 t ^{3}}{3} - 10 t + c_{1}, x = - \frac{2 t ^{3}}{3} - 10 t + c_{1}

x = \frac{2 t ^{3}}{3} - 10 t + c_{1}, x = - \frac{2 t ^{3}}{3} - 10 t + c_{1}

\frac{d y}{d t} = 100 - y, y (0) = 20

\frac{d x}{d t} = 30 - 11 x + x^{2}

\frac{d}{d x} (x y) = \frac{d}{d x} (x + y)

\frac{d}{d x} ((x) y) = (y) x

\frac{d}{d x} (z (x) \cdot e^{2 x}) = e^{2 x}

What is the solution for (dx)/(dt)x=t^2-5 ?
The solution for (dx)/(dt)x=t^2-5 is x=sqrt((2t^3)/3-10t+c_{1)},x=-sqrt((2t^3)/3-10t+c_{1)}