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Beliebt Rechnen >

9y^{''}+4y=3x+12e^{-x}

Lösung

9 y^{^{''}} + 4 y = 3 x + 12 e^{- x}

Lösung

y = c_{1} cos (\frac{2 x}{3}) + c_{2} sin (\frac{2 x}{3}) + \frac{3 x}{4} + \frac{12}{13} e^{- x}

Schritte zur Lösung

9 y^{''} (x) + 4 y = 3 x + 12 e^{- x}

Solve linear ODE:

y = c_{1} cos (\frac{2 x}{3}) + c_{2} sin (\frac{2 x}{3}) + \frac{3 x}{4} + \frac{12}{13} e^{- x}

y = c_{1} cos (\frac{2 x}{3}) + c_{2} sin (\frac{2 x}{3}) + \frac{3 x}{4} + \frac{12}{13} e^{- x}

Graph

Beliebte Beispiele

y^{''''}+8y^{''}+16y=-sin(x)

y^{^{''''}} + 8 y^{^{''}} + 16 y = - sin (x)

x^{''}+6x^'+23x=12cos(4t)

x^{^{''}} + 6 x^{^{'}} + 23 x = 12 cos (4 t)

(d^2+9)y=30sin^3(x)

(d^{2} + 9) y = 30 sin^{3} (x)

y^{''''}-y=11t+cos(t)

y^{^{''''}} - y = 11 t + cos (t)

y^{''}-4y^'+4y=10e^{2x}

y^{^{''}} - 4 y^{^{'}} + 4 y = 10 e^{2 x}