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Beliebt Rechnen >

(dy)/(dx)=(xy^3-y^3)/(e^x)

Lösung

\frac{d y}{d x} = \frac{x y ^{3} - y ^{3}}{e ^{x}}

Lösung

y = - \frac{e ^{x}}{2 ( - x + c _{1} e ^{x} )}, y = - - \frac{e ^{x}}{2 ( - x + c _{1} e ^{x} )}

Schritte zur Lösung

\frac{d y}{d x} = \frac{x y ^{3} - y ^{3}}{e ^{x}}

Solve separable ODE:

y = - \frac{e ^{x}}{2 ( - x + c _{1} e ^{x} )}, y = - - \frac{e ^{x}}{2 ( - x + c _{1} e ^{x} )}

y = - \frac{e ^{x}}{2 ( - x + c _{1} e ^{x} )}, y = - - \frac{e ^{x}}{2 ( - x + c _{1} e ^{x} )}

Graph

Beliebte Beispiele

y^'+x/(x^2-9)*y=0

y^{^{'}} + \frac{x}{x ^{2} - 9} \cdot y = 0

(dx)/(dt)=10-x/(10)

\frac{d x}{d t} = 10 - \frac{x}{10}

y^'= y/(x+xe^x)

y^{^{'}} = \frac{y}{x + x e ^{x}}

(t^2+1)dy+3tydt=6tdt,y(0)=5

(t^{2} + 1) d y + 3 t y d t = 6 t d t, y (0) = 5

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

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