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

Lösung

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

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{3}}{6} + \frac{- x ^{2} + x}{4} - \frac{e ^{- 2 x} x}{2}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{3}}{6} + \frac{- x ^{2} + x}{4} - \frac{e ^{- 2 x} x}{2}

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{3}}{6} + \frac{- x ^{2} + x}{4} - \frac{e ^{- 2 x} x}{2}

t an g e n t f (x) = x, at x = 64.2

x \to 3 lim (6 x^{2} + 2)

\int \frac{( x + 1 )}{x ^{2} + 2 x - 4} d x

\int_{1}^{100} \frac{25}{x ^{3}} d x

\int_{0}^{x^{3}} y e^{- \frac{y}{x}} d y