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Beliebt Rechnen >

y^{'''}+y=4e^x

Lösung

y^{^{'''}} + y = 4 e^{x}

Lösung

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

Schritte zur Lösung

y^{'''} (x) + y = 4 e^{x}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

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

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

y^{''}+2y^'+10y=50x,y(0)=1,y^'(0)=0

y^{^{''}} + 2 y^{^{'}} + 10 y = 50 x, y (0) = 1, y^{^{'}} (0) = 0

y^{''}+3y^'=(10sin(7t))/2

y^{^{''}} + 3 y^{^{'}} = \frac{10 sin ( 7 t )}{2}

y^{''}-4y^'+3y=(e^t)/(1+e^t)

y^{^{''}} - 4 y^{^{'}} + 3 y = \frac{e ^{t}}{1 + e ^{t}}

(d^2y)/(dt^2)+9y=12cos(3t)

\frac{d ^{2} y}{d t ^{2}} + 9 y = 12 cos (3 t)