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Beliebt Rechnen >

(dy)/(dx)-(xy)/(1+x)=x

Lösung

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

Lösung

y = \frac{\int x ( e ^{- 1 - x + c_{1}} + e ^{- 1 - x + c_{1}} x ) d x}{e ^{- 1 - x + c_{1}} + e ^{- 1 - x + c_{1}} x}

Schritte zur Lösung

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

Solve linear ODE:

y = \frac{\int x ( e ^{- 1 - x + c_{1}} + e ^{- 1 - x + c_{1}} x ) d x}{e ^{- 1 - x + c_{1}} + e ^{- 1 - x + c_{1}} x}

y = \frac{\int x ( e ^{- 1 - x + c_{1}} + e ^{- 1 - x + c_{1}} x ) d x}{e ^{- 1 - x + c_{1}} + e ^{- 1 - x + c_{1}} x}

Beliebte Beispiele

(\partial)/(\partial x)(ln(4x^2+9y^2+8))

\frac{\partial}{\partial x} (ln (4 x^{2} + 9 y^{2} + 8))

y^{^{''}} + 2 y = 1

y^{''}+2y=sin(xsqrt(2))

y^{^{''}} + 2 y = sin (x 2)

tangent f(x)=4x^2+12x+7,\at x=-2

t an g e n t f (x) = 4 x^{2} + 12 x + 7, at x = - 2

derivative x^2-sqrt(x)

d er i v a t i v e x^{2} - x