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Beliebt Rechnen >

(dy)/(dx)=2sqrt(xy),y(1)=5

Lösung

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

Lösung

y = \frac{4}{9} - \frac{4 5}{3} + \frac{4 x ^{3}}{9} - \frac{8 x ^{\frac{3}{2}}}{9} + \frac{4 5 x ^{\frac{3}{2}}}{3} + 5

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{4}{9} - \frac{4 5}{3} + \frac{4 x ^{3}}{9} - \frac{8 x ^{\frac{3}{2}}}{9} + \frac{4 5 x ^{\frac{3}{2}}}{3} + 5

y = \frac{4}{9} - \frac{4 5}{3} + \frac{4 x ^{3}}{9} - \frac{8 x ^{\frac{3}{2}}}{9} + \frac{4 5 x ^{\frac{3}{2}}}{3} + 5

Graph

Beliebte Beispiele

x^'=20t-(4x)/(30)t

x^{^{'}} = 20 t - \frac{4 x}{30} t

2xy(dy)/(dx)=6+14ln(x)

2 x y \frac{d y}{d x} = 6 + 14 ln (x)

(1+x^2)(dy)/(dx)=sin(y)

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

ydx-xdy=y^3+y^2xdy

y d x - x d y = y^{3} + y^{2} x d y

derivative of 3y^2+2x^3-14=0

\frac{d}{d x} (3 y^{2}) + 2 x^{3} - 14 = 0