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Beliebt Rechnen >

y^{''}+9y=t^2e^3t+6

Lösung

y^{^{''}} + 9 y = t^{2} e^{3} t + 6

Lösung

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{e ^{3} t ^{3}}{9} - \frac{2 e ^{3} t}{27} + \frac{2}{3}

Schritte zur Lösung

y^{''} (t) + 9 y = t^{2} e^{3} t + 6

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{e ^{3} t ^{3}}{9} - \frac{2 e ^{3} t}{27} + \frac{2}{3}

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{e ^{3} t ^{3}}{9} - \frac{2 e ^{3} t}{27} + \frac{2}{3}

Graph

Beliebte Beispiele

inverselaplace 1/((s-3)(s+1))

in v erse l a pl a ce \frac{1}{( s - 3 ) ( s + 1 )}

integral of (3x-y)/9

\int \frac{3 x - y}{9} d y

y^{''}-14y^'+49y=3t^{-1}e^{7t}

y^{^{''}} - 14 y^{^{'}} + 49 y = 3 t^{- 1} e^{7 t}

steigung (-3,4),(2,-9)

s l o p e (- 3, 4), (2, - 9)

integral of tan^{-3/2}(x)sec^4(x)

\int tan^{- \frac{3}{2}} (x) sec^{4} (x) d x