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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

derivative y=2xsin(x)

d er i v a t i v e y = 2 x sin (x)

limit as x approaches 0 of (4x)/(|x|)

x \to 0 lim (\frac{4 x}{∣ x ∣})

y^{^{''}} - 8 y^{^{'}} = 5 t

y^{''}+4y^'+4y=12t+16,y(0)=3,y^'(0)=-4

y^{^{''}} + 4 y^{^{'}} + 4 y = 12 t + 16, y (0) = 3, y^{^{'}} (0) = - 4

derivative of (2^0/(3^1+0))

\frac{d}{d x} (\frac{2 ^{0}}{3 ^{1} + 0})