y^{''}+7y^'+10y=14xe^{3x}

Lösung

y^{^{''}} + 7 y^{^{'}} + 10 y = 14 x e^{3 x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 5 x} + \frac{7 e ^{3 x} x}{20} - \frac{91}{800} e^{3 x}

Schritte zur Lösung

y^{''} (x) + 7 y^{'} (x) + 10 y = 14 x e^{3 x}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{- 5 x} + \frac{7 e ^{3 x} x}{20} - \frac{91}{800} e^{3 x}

y = c_{1} e^{- 2 x} + c_{2} e^{- 5 x} + \frac{7 e ^{3 x} x}{20} - \frac{91}{800} e^{3 x}

im pl i c i t \frac{d u}{d v}, u + v = 5

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\int \frac{x ^{2} - 11 x - 18}{x ( x ^{2} + 3 x + 3 )} d x

\frac{\partial}{\partial x} (5 x y - 4 x^{2} y)

\frac{\partial}{\partial x} (x)