(dv)/(dt)v=(2^{5/2})t^{3/2}+3

Lösung

\frac{d v}{d t} v = (2^{\frac{5}{2}}) t^{\frac{3}{2}} + 3

v = \frac{16 \cdot 2 ^{\frac{1}{2}}}{5} t^{\frac{5}{2}} + 6 t + c_{1}, v = - \frac{16 \cdot 2 ^{\frac{1}{2}}}{5} t^{\frac{5}{2}} + 6 t + c_{1}

Schritte zur Lösung

\frac{d v}{d t} v = (2^{\frac{5}{2}}) t^{\frac{3}{2}} + 3

Solve separable ODE:

v = \frac{16 \cdot 2 ^{\frac{1}{2}}}{5} t^{\frac{5}{2}} + 6 t + c_{1}, v = - \frac{16 \cdot 2 ^{\frac{1}{2}}}{5} t^{\frac{5}{2}} + 6 t + c_{1}

v = \frac{16 \cdot 2 ^{\frac{1}{2}}}{5} t^{\frac{5}{2}} + 6 t + c_{1}, v = - \frac{16 \cdot 2 ^{\frac{1}{2}}}{5} t^{\frac{5}{2}} + 6 t + c_{1}

\frac{d y}{d x} (sin (π) x + cos (π) y)^{2} = 2

x^{2} y - 3 x y^{^{'}} + 4 y = 0

(x^{2} + 1) y^{^{'}} = x y ln (y)

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

\frac{4}{x} + \frac{\frac{d y}{d x}}{2 y} = 0