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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{13} e^{3 x} - \frac{x ^{2} cos ( 2 x )}{8} + \frac{x sin ( 2 x )}{16}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{13} e^{3 x} - \frac{x ^{2} cos ( 2 x )}{8} + \frac{x sin ( 2 x )}{16}

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{13} e^{3 x} - \frac{x ^{2} cos ( 2 x )}{8} + \frac{x sin ( 2 x )}{16}

Graph

Beliebte Beispiele

y^{''}+3y^'+2y= 1/((1+e^x))

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{( 1 + e ^{x} )}

y^{'''}-9y^{''}+108y=e^{6x}

y^{^{'''}} - 9 y^{^{''}} + 108 y = e^{6 x}

y^{^{''}} + y^{^{'}} + y = x

(d^2y)/(dt^2)-y=e^t

\frac{d ^{2} y}{d t ^{2}} - y = e^{t}

x^{''}-5x^'+4x=8e^t

x^{^{''}} - 5 x^{^{'}} + 4 x = 8 e^{t}