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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+4y+4y=(3+x)e^{-2x}

y^{^{''}} + 4 y + 4 y = (3 + x) e^{- 2 x}

y^{''}-6y^'+8y=3e^{-2x}+2x

y^{^{''}} - 6 y^{^{'}} + 8 y = 3 e^{- 2 x} + 2 x

x^{''}+4x^'+3x=1

x^{^{''}} + 4 x^{^{'}} + 3 x = 1

(D-1)^2y=(e^{2x}+sin(2x))

(D - 1)^{2} y = (e^{2 x} + sin (2 x))

y^{''}-2y^'-3y=3te^{2t},y(0)=3,y^'(0)=0

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 t e^{2 t}, y (0) = 3, y^{^{'}} (0) = 0