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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{3 e ^{2 x} x ^{2}}{2} + \frac{3 x sin ( x ) + 4 x cos ( x )}{25} + \frac{4}{125} sin (x) + \frac{22}{125} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{3 e ^{2 x} x ^{2}}{2} + \frac{3 x sin ( x ) + 4 x cos ( x )}{25} + \frac{4}{125} sin (x) + \frac{22}{125} cos (x)

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{3 e ^{2 x} x ^{2}}{2} + \frac{3 x sin ( x ) + 4 x cos ( x )}{25} + \frac{4}{125} sin (x) + \frac{22}{125} cos (x)

Graph

Beliebte Beispiele

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

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

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

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

(d^2-3d)y=x^2+2x-6

(d^{2} - 3 d) y = x^{2} + 2 x - 6

y^{''}+y=-8xcos(x)

y^{^{''}} + y = - 8 x cos (x)

x^{''}-x^'-12x=2sinh^2(t)

x^{^{''}} - x^{^{'}} - 12 x = 2 sinh^{2} (t)