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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x ^{2} cos ( 2 x )}{4} + \frac{x sin ( 2 x )}{8}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x ^{2} cos ( 2 x )}{4} + \frac{x sin ( 2 x )}{8}

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{x ^{2} cos ( 2 x )}{4} + \frac{x sin ( 2 x )}{8}

Graph

Beliebte Beispiele

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

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

4y^{''}-4y^'+y=16e^{x/2}

4 y^{^{''}} - 4 y^{^{'}} + y = 16 e^{\frac{x}{2}}

y^{''}-y^'=e^xsin(x)

y^{^{''}} - y^{^{'}} = e^{x} sin (x)

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

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

y^{'''}-y^{''}-4y^'+4y=20e^{3t}

y^{^{'''}} - y^{^{''}} - 4 y^{^{'}} + 4 y = 20 e^{3 t}