(dP)/(dt)=5sqrt(Pt),P(1)=5

Lösung

\frac{d P}{d t} = 5 Pt, P (1) = 5

P = \frac{25}{9} - \frac{10 5}{3} + \frac{25 t ^{3}}{9} - \frac{50 t ^{\frac{3}{2}}}{9} + \frac{10 5 t ^{\frac{3}{2}}}{3} + 5

Schritte zur Lösung

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

Solve separable ODE:

P = \frac{25}{9} - \frac{10 5}{3} + \frac{25 t ^{3}}{9} - \frac{50 t ^{\frac{3}{2}}}{9} + \frac{10 5 t ^{\frac{3}{2}}}{3} + 5

P = \frac{25}{9} - \frac{10 5}{3} + \frac{25 t ^{3}}{9} - \frac{50 t ^{\frac{3}{2}}}{9} + \frac{10 5 t ^{\frac{3}{2}}}{3} + 5

cos (y) (2 ln (x) - x^{3}) \frac{d y}{d x} = \frac{2}{x} - 3 x^{2}

\frac{d y}{d x} y = - arccot (\frac{6 x}{3})

\frac{d y}{d x} = - x y + \frac{4 x}{y}

\frac{d y}{d x} = 9 x^{2} y^{2}, y \neq = 0

t y^{^{'}} + 2 y = 0