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}

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