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Beliebt Rechnen >

(d^2-4d+4)y=8e^{2x}x^2*sin^2(x)

Lösung

(d^{2} - 4 d + 4) \cdot y = 8 e^{2 x} \cdot x^{2} \cdot sin^{2} (x)

Lösung

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{2}{3} e^{2 x} x^{4} sin^{2} (x) + \frac{1}{3} e^{2 x} x^{4} cos (2 x) + e^{2 x} x^{2} cos (2 x) - 2 e^{2 x} x sin (2 x) - \frac{3}{2} e^{2 x} cos (2 x)

Schritte zur Lösung

(d^{2} - 4 d + 4) y = 8 e^{2 x} x^{2} sin^{2} (x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{2}{3} e^{2 x} x^{4} sin^{2} (x) + \frac{1}{3} e^{2 x} x^{4} cos (2 x) + e^{2 x} x^{2} cos (2 x) - 2 e^{2 x} x sin (2 x) - \frac{3}{2} e^{2 x} cos (2 x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{2}{3} e^{2 x} x^{4} sin^{2} (x) + \frac{1}{3} e^{2 x} x^{4} cos (2 x) + e^{2 x} x^{2} cos (2 x) - 2 e^{2 x} x sin (2 x) - \frac{3}{2} e^{2 x} cos (2 x)

Graph

Beliebte Beispiele

y^{''}-3y^'+2y=4t-8

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 t - 8

(d^3-2d+4)y=3x^2-5x+2

(d^{3} - 2 d + 4) y = 3 x^{2} - 5 x + 2

(d^3-3d^2+4d-2)*y=e^x+cos(x)+x

(d^{3} - 3 d^{2} + 4 d - 2) \cdot y = e^{x} + cos (x) + x

(d^4+d^2+16)y=16x^2+256

(d^{4} + d^{2} + 16) y = 16 x^{2} + 256

y^{''}+10y^'+25y=e^{-5}x

y^{^{''}} + 10 y^{^{'}} + 25 y = e^{- 5} x