What is the solution for (dv}{dt}=\frac{0.1)/v*(0.25)/t ?

The solution for (dv}{dt}=\frac{0.1)/v*(0.25)/t is v=sqrt(0.05ln(t)+c_{1)},v=-sqrt(0.05ln(t)+c_{1)}

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(dv}{dt}=\frac{0.1)/v*(0.25)/t

\frac{d v}{d t} = \frac{0.1}{v} \cdot \frac{0.25}{t}

v = 0.05 ln (t) + c_{1}, v = - 0.05 ln (t) + c_{1}

Solution steps

\frac{d v}{d t} = \frac{0.1}{v} \cdot \frac{0.25}{t}

Solve separable ODE:

v = 0.05 ln (t) + c_{1}, v = - 0.05 ln (t) + c_{1}

v = 0.05 ln (t) + c_{1}, v = - 0.05 ln (t) + c_{1}

y \frac{d y}{d x} = 3, x (y^{2} + 6)^{8} = 3

\frac{d y}{d x} = (1 + x^{2}) (1 + y)

y^{2} y^{^{'}} = - 2 x y, y (0) = 2

\frac{d y}{d x} = \frac{x - 5}{y}

\frac{d y}{d x} = - \frac{3}{4} x^{4} y^{3}

What is the solution for (dv}{dt}=\frac{0.1)/v*(0.25)/t ?
The solution for (dv}{dt}=\frac{0.1)/v*(0.25)/t is v=sqrt(0.05ln(t)+c_{1)},v=-sqrt(0.05ln(t)+c_{1)}