What is the solution for (dP)/(dt)=5sqrt(Pt) ?

The solution for (dP)/(dt)=5sqrt(Pt) is P=(25t^3)/9+(5c_{1}t^{3/2})/3+(c_{1}^2)/4

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(dP)/(dt)=5sqrt(Pt)

\frac{d P}{d t} = 5 Pt

P = \frac{25 t ^{3}}{9} + \frac{5 c _{1} t ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d P}{d t} = 5 Pt

Solve separable ODE:

P = \frac{25 t ^{3}}{9} + \frac{5 c _{1} t ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

P = \frac{25 t ^{3}}{9} + \frac{5 c _{1} t ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

\frac{d}{d x} ((3 x + 1) (2 x + 6))

y = x^{3} - 5 x, (- 1, 5)

\int x^{3} e^{x^{2} + 1} d x

\frac{d}{d x} (2 ln (x y))

\int - x^{0} d x

What is the solution for (dP)/(dt)=5sqrt(Pt) ?
The solution for (dP)/(dt)=5sqrt(Pt) is P=(25t^3)/9+(5c_{1}t^{3/2})/3+(c_{1}^2)/4