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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+4y=t^2+10e^t

y^{^{''}} + 4 y = t^{2} + 10 e^{t}

y^{''}-y=1.7sin(t)

y^{^{''}} - y = 1.7 sin (t)

1/2 x^{''}+2x^'+4x=20cos(t)

\frac{1}{2} x^{^{''}} + 2 x^{^{'}} + 4 x = 20 cos (t)

2y^{''}+8y^'+80y=40cos(8x)

2 y^{^{''}} + 8 y^{^{'}} + 80 y = 40 cos (8 x)

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

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