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Beliebt Rechnen >

4y^{''}-40y^'+100y=2sin(2x)+5cos(2x)

Lösung

4 y^{^{''}} - 40 y^{^{'}} + 100 y = 2 sin (2 x) + 5 cos (2 x)

Lösung

y = c_{1} e^{5 x} + c_{2} x e^{5 x} - \frac{1}{58} sin (2 x) + \frac{5}{116} cos (2 x)

Schritte zur Lösung

4 y^{''} (x) - 40 y^{'} (x) + 100 y = 2 sin (2 x) + 5 cos (2 x)

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} x e^{5 x} - \frac{1}{58} sin (2 x) + \frac{5}{116} cos (2 x)

y = c_{1} e^{5 x} + c_{2} x e^{5 x} - \frac{1}{58} sin (2 x) + \frac{5}{116} cos (2 x)

Graph

Beliebte Beispiele

y^{^{''}} - 4 y + 5 = 0

4y^{''}-y=1,y^'(0)= 1/2 ,y(0)=0

4 y^{^{''}} - y = 1, y^{^{'}} (0) = \frac{1}{2}, y (0) = 0

y^{''}-y^'-20=0

y^{^{''}} - y^{^{'}} - 20 = 0

(d^2y)/(dx^2)-9y=e^{3x}cos(2x)+e^{2x}

\frac{d ^{2} y}{d x ^{2}} - 9 y = e^{3 x} cos (2 x) + e^{2 x}

y^{''}+9y=cos(t)

y^{^{''}} + 9 y = cos (t)