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Beliebt Rechnen >

(dy)/(dx)+xy=xy^{-1/2}

Lösung

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

Lösung

y = 3 e^{\frac{- 3 x ^{2} - 6 c _{1}}{2}} - 2 e^{- \frac{3 x ^{2}}{4} - \frac{3 c _{1}}{2}} + 1

Schritte zur Lösung

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

Solve separable ODE:

y = 3 e^{\frac{- 3 x ^{2} - 6 c _{1}}{2}} - 2 e^{- \frac{3 x ^{2}}{4} - \frac{3 c _{1}}{2}} + 1

y = 3 e^{\frac{- 3 x ^{2} - 6 c _{1}}{2}} - 2 e^{- \frac{3 x ^{2}}{4} - \frac{3 c _{1}}{2}} + 1

Graph

Beliebte Beispiele

(dx)/(dt)=37.5-3.5x

\frac{d x}{d t} = 37.5 - 3.5 x

(x+1)ydx+y^2e^xdy=0

(x + 1) y d x + y^{2} e^{x} d y = 0

(dy)/(dx)=(4x+xy^2)/(2y+x^2y)

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

(2x+1)dx+(5-6y)dy=0

(2 x + 1) d x + (5 - 6 y) d y = 0

y^'=12y^{-2},y(0)=3

y^{^{'}} = 12 y^{- 2}, y (0) = 3