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Beliebt Rechnen >

y^{''}-y^'+y=25sin(2x)

Lösung

y^{^{''}} - y^{^{'}} + y = 25 sin (2 x)

Lösung

y = e^{\frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) - \frac{75}{13} sin (2 x) + \frac{50}{13} cos (2 x)

Schritte zur Lösung

y^{''} (x) - y^{'} (x) + y = 25 sin (2 x)

Solve linear ODE:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) - \frac{75}{13} sin (2 x) + \frac{50}{13} cos (2 x)

y = e^{\frac{x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) - \frac{75}{13} sin (2 x) + \frac{50}{13} cos (2 x)

Graph

Beliebte Beispiele

y^{''}-2y^'+y=(e^x)/((1-x)^2)

y^{''}-8y^'+16y=2e^{4t}cos(5t)

a^2y^{''}-(a^2+1)y^'+y=x

(d^2y)/(dx^2)-4(dy)/(dx)-12y=3e^{5x}