(dy)/(dx)=sqrt(yx),y(1)=7

Lösung

\frac{d y}{d x} = y x, y (1) = 7

y = \frac{1}{9} + \frac{x ^{3}}{9} - \frac{2 7}{3} - \frac{2 x ^{\frac{3}{2}}}{9} + \frac{2 7 x ^{\frac{3}{2}}}{3} + 7

Schritte zur Lösung

\frac{d y}{d x} = y x

Solve separable ODE:

y = \frac{1}{9} + \frac{x ^{3}}{9} - \frac{2 7}{3} - \frac{2 x ^{\frac{3}{2}}}{9} + \frac{2 7 x ^{\frac{3}{2}}}{3} + 7

y = \frac{1}{9} + \frac{x ^{3}}{9} - \frac{2 7}{3} - \frac{2 x ^{\frac{3}{2}}}{9} + \frac{2 7 x ^{\frac{3}{2}}}{3} + 7

\frac{d y}{d x} = \frac{( 4 x e ^{x^{2}} )}{y}, y (0) = 3

\frac{d y}{d x} = - y (x^{2} - 7)

\frac{1}{y} \cdot \frac{d y}{d t} = 0.02

y \frac{d x}{d y} - x = 2, y^{2} y (1) = 5

y^{^{'}} + \frac{1}{2} (x - 2) y^{2} = 0, y (\frac{1}{10}) = 6