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Beliebt Rechnen >

(D^2-3D+2)y=xe^x

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+y=8sin(x)+4cos(x)+1

y^{^{''}} + y = 8 sin (x) + 4 cos (x) + 1

x^{''}+4x^'+4=0

x^{^{''}} + 4 x^{^{'}} + 4 = 0

y^{''}-2y^'+y=(e^t)/((1+t^2)+3e^t)

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{( 1 + t ^{2} ) + 3 e ^{t}}

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

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

y^{''}+2y^'+2y=4cos(t)+2sin(t)

y^{^{''}} + 2 y^{^{'}} + 2 y = 4 cos (t) + 2 sin (t)