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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + \frac{9 x sin ( x )}{25} - \frac{12 x cos ( x )}{25} + \frac{72}{125} sin (x) + \frac{104}{125} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + \frac{9 x sin ( x )}{25} - \frac{12 x cos ( x )}{25} + \frac{72}{125} sin (x) + \frac{104}{125} cos (x)

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + \frac{9 x sin ( x )}{25} - \frac{12 x cos ( x )}{25} + \frac{72}{125} sin (x) + \frac{104}{125} cos (x)

Graph

Beliebte Beispiele

y^{^{''}} + y^{^{'}} - 6 = 0

y^{''}-2y^'+65y=e^xcos(8x)

y^{^{''}} - 2 y^{^{'}} + 65 y = e^{x} cos (8 x)

x^{''}+8x=16cos(4t)

x^{^{''}} + 8 x = 16 cos (4 t)

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

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

y^{''}-8y^'+2y=xe^x

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