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Beliebt Rechnen >

y^{''}-6y^'+25y=30e^{3x}sin(x)

Lösung

y^{^{''}} - 6 y^{^{'}} + 25 y = 30 e^{3 x} sin (x)

Lösung

y = e^{3 x} (c_{1} cos (4 x) + c_{2} sin (4 x)) + 2 e^{3 x} sin (x)

Schritte zur Lösung

y^{''} (x) - 6 y^{'} (x) + 25 y = 30 e^{3 x} sin (x)

Solve linear ODE:

y = e^{3 x} (c_{1} cos (4 x) + c_{2} sin (4 x)) + 2 e^{3 x} sin (x)

y = e^{3 x} (c_{1} cos (4 x) + c_{2} sin (4 x)) + 2 e^{3 x} sin (x)

Graph

Beliebte Beispiele

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

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

y^{''}+2y^'+10y=2cos(6x)

y^{^{''}} + 2 y^{^{'}} + 10 y = 2 cos (6 x)

6y^{''}-3y=x^2-x+7

6 y^{^{''}} - 3 y = x^{2} - x + 7

y^{''}+4y=x^2+5cos(2x)

y^{^{''}} + 4 y = x^{2} + 5 cos (2 x)

(d^2y)/(dx^2)-3(dy)/(dx)+2y=4x+6

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 4 x + 6