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Beliebt Rechnen >

y^{''}+3y^'+2y= 1/(2+e^x)

Lösung

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{2 + e ^{x}}

Lösung

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + ln (2 + e^{x}) e^{- x} + (- 2 - e^{x} + 2 ln (2 + e^{x})) e^{- 2 x}

Schritte zur Lösung

y^{''} (x) + 3 y^{'} (x) + 2 y = \frac{1}{2 + e ^{x}}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + ln (2 + e^{x}) e^{- x} + (- 2 - e^{x} + 2 ln (2 + e^{x})) e^{- 2 x}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + ln (2 + e^{x}) e^{- x} + (- 2 - e^{x} + 2 ln (2 + e^{x})) e^{- 2 x}

Graph

Beliebte Beispiele

tangent f(x)=(1+4x)^{3/2},\at x=2

t an g e n t f (x) = (1 + 4 x)^{\frac{3}{2}}, at x = 2

derivative y=x^2-5x-3

d er i v a t i v e y = x^{2} - 5 x - 3

derivative of (tan^2(x)/2)

\frac{d}{d x} (\frac{tan ^{2} ( x )}{2})

derivative of e^{3x+3}

\frac{d}{d x} (e^{3 x + 3})

integral of 1/(2x^2-5x+7)

\int \frac{1}{2 x ^{2} - 5 x + 7} d x