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Beliebt Rechnen >

y^{''}+9y=t^2e^{3t}

Lösung

y^{^{''}} + 9 y = t^{2} e^{3 t}

Lösung

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{e ^{3 t} t ^{2}}{18} - \frac{e ^{3 t} t}{27} + \frac{1}{162} e^{3 t}

Schritte zur Lösung

y^{''} (t) + 9 y = t^{2} e^{3 t}

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{e ^{3 t} t ^{2}}{18} - \frac{e ^{3 t} t}{27} + \frac{1}{162} e^{3 t}

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{e ^{3 t} t ^{2}}{18} - \frac{e ^{3 t} t}{27} + \frac{1}{162} e^{3 t}

Graph

Beliebte Beispiele

y^{''}+16y=8cos(4x)+12sin(4x)

y^{^{''}} + 16 y = 8 cos (4 x) + 12 sin (4 x)

(d^2x)/(dt^2)+9x=5sin(3t)

\frac{d ^{2} x}{d t ^{2}} + 9 x = 5 sin (3 t)

y^{''}-2y^'-3y=(3x^2-5)e^{-x}

y^{^{''}} - 2 y^{^{'}} - 3 y = (3 x^{2} - 5) e^{- x}

2y^{''}-8y=16e^x

2 y^{^{''}} - 8 y = 16 e^{x}

(d^3-3d-2)y=540x^3e^{-x}

(d^{3} - 3 d - 2) y = 540 x^{3} e^{- x}