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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{x} + c_{2} x e^{x} - 2 x^{2} e^{x} + 3 x^{2} + 12 x + 18

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} - 2 x^{2} e^{x} + 3 x^{2} + 12 x + 18

y = c_{1} e^{x} + c_{2} x e^{x} - 2 x^{2} e^{x} + 3 x^{2} + 12 x + 18

Graph

Beliebte Beispiele

y^{''}+3y^'+4y=8x+2

y^{^{''}} + 3 y^{^{'}} + 4 y = 8 x + 2

(d^2+d)y=x^2+2x-3

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

2y^{''}+12y=6tan(3x)

2 y^{^{''}} + 12 y = 6 tan (3 x)

y^{''}+4y^'+5y=-5x+3e^{(-x)}

y^{^{''}} + 4 y^{^{'}} + 5 y = - 5 x + 3 e^{(- x)}

y^{''}-3y^'+2y=11e^3x,y^1(0)=ex

y^{^{''}} - 3 y^{^{'}} + 2 y = 11 e^{3} x, y^{1} (0) = e x