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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{- x} + c_{2} x e^{- x} + (- \frac{6}{5} (x + 1)^{\frac{5}{2}} + 2 (x + 1)^{\frac{3}{2}}) e^{- x} + 2 (x + 1)^{\frac{3}{2}} e^{- x} x

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} x e^{- x} + (- \frac{6}{5} (x + 1)^{\frac{5}{2}} + 2 (x + 1)^{\frac{3}{2}}) e^{- x} + 2 (x + 1)^{\frac{3}{2}} e^{- x} x

y = c_{1} e^{- x} + c_{2} x e^{- x} + (- \frac{6}{5} (x + 1)^{\frac{5}{2}} + 2 (x + 1)^{\frac{3}{2}}) e^{- x} + 2 (x + 1)^{\frac{3}{2}} e^{- x} x

Graph

Beliebte Beispiele

f (t) = ln (t^{2} + 1)

sum from n=6 to infinity of e^{3-2n}

n = 6 \sum \infty e^{3 - 2 n}

x^2y^{''}+xy^'=0

x^{2} y^{^{''}} + x y^{^{'}} = 0

derivative of 3x^2log_{3}(x)

\frac{d}{d x} (3 x^{2} lo g_{3} (x))

limit as k approaches 0 of (x^2k+3xk^2+k^2)/(2xk+5k^2)

k \to 0 lim (\frac{x ^{2} k + 3 x k ^{2} + k ^{2}}{2 x k + 5 k ^{2}})