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Beliebt Rechnen >

y^{''}-y^'+25y=5sin(5t)

Lösung

y^{^{''}} - y^{^{'}} + 25 y = 5 sin (5 t)

Lösung

y = e^{\frac{t}{2}} (c_{1} cos (\frac{3 11 t}{2}) + c_{2} sin (\frac{3 11 t}{2})) + cos (5 t)

Schritte zur Lösung

y^{''} (t) - y^{'} (t) + 25 y = 5 sin (5 t)

Solve linear ODE:

y = e^{\frac{t}{2}} (c_{1} cos (\frac{3 11 t}{2}) + c_{2} sin (\frac{3 11 t}{2})) + cos (5 t)

y = e^{\frac{t}{2}} (c_{1} cos (\frac{3 11 t}{2}) + c_{2} sin (\frac{3 11 t}{2})) + cos (5 t)

Graph

Beliebte Beispiele

y^{''}-6y^'+9y=e^tcos(t)

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{t} cos (t)

y^{''}+4y^'-2y=8sin(2x)

y^{^{''}} + 4 y^{^{'}} - 2 y = 8 sin (2 x)

y^{''}-3y^'+2y=4t+12e^{-t}

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 t + 12 e^{- t}

y^{''}-64y=cosh(8x)

y^{^{''}} - 64 y = cosh (8 x)

y^{''}-2y^'+y=(5e^t)/(1+t^2)

y^{^{''}} - 2 y^{^{'}} + y = \frac{5 e ^{t}}{1 + t ^{2}}