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Beliebt Rechnen >

y^{''}-8y^'+15y=e^{3x}sin(3x)

Lösung

y^{^{''}} - 8 y^{^{'}} + 15 y = e^{3 x} sin (3 x)

Lösung

y = c_{1} e^{5 x} + c_{2} e^{3 x} + \frac{2}{39} e^{3 x} cos (3 x) - \frac{1}{13} e^{3 x} sin (3 x)

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 15 y = e^{3 x} sin (3 x)

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{3 x} + \frac{2}{39} e^{3 x} cos (3 x) - \frac{1}{13} e^{3 x} sin (3 x)

y = c_{1} e^{5 x} + c_{2} e^{3 x} + \frac{2}{39} e^{3 x} cos (3 x) - \frac{1}{13} e^{3 x} sin (3 x)

Graph

Beliebte Beispiele

x^{''}+a^2x=a^2b+c

x^{^{''}} + a^{2} x = a^{2} b + c

y^{''}-10y^'+9y=5

y^{^{''}} - 10 y^{^{'}} + 9 y = 5

y^{''}-8y^'+20y=200x^2-78xe^x

y^{^{''}} - 8 y^{^{'}} + 20 y = 200 x^{2} - 78 x e^{x}

y^{''}+y^'-12y=2cos(t)

y^{^{''}} + y^{^{'}} - 12 y = 2 cos (t)

D^2(D-1)y=8e^{2x}

D^{2} (D - 1) y = 8 e^{2 x}