What is the solution for (dv)/(dt)=sqrt(9v),v(0)=11.3 ?

The solution for (dv)/(dt)=sqrt(9v),v(0)=11.3 is v=2.25t^2+10.08464…t+11.3

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(dv)/(dt)=sqrt(9v),v(0)=11.3

\frac{d v}{d t} = 9 v, v (0) = 11.3

v = 2.25 t^{2} + 10.08464 \dots t + 11.3

Solution steps

\frac{d v}{d t} = 9 v

Solve separable ODE:

v = 2.25 t^{2} + 10.08464 \dots t + 11.3

v = 2.25 t^{2} + 10.08464 \dots t + 11.3

y^{^{'}} = cot (y) sin (x)

(x y^{3} - x) d x + x y^{2} d y = 0

\frac{d y}{d x} = x y^{3} (1 + x^{2})^{\frac{- 1}{2}}

e^{2} x y^{^{'}} + 2 e^{2} x y = 2 x

\frac{d y}{d x} = 2 e^{x - y}, y (0) = ln (9)

What is the solution for (dv)/(dt)=sqrt(9v),v(0)=11.3 ?
The solution for (dv)/(dt)=sqrt(9v),v(0)=11.3 is v=2.25t^2+10.08464…t+11.3