y^{''}-7y^'+3y=xe^x

Lösung

y^{^{''}} - 7 y^{^{'}} + 3 y = x e^{x}

y = c_{1} e^{\frac{( 7 + 37 ) x}{2}} + c_{2} e^{\frac{( 7 - 37 ) x}{2}} - \frac{e ^{x} x}{3} + \frac{5}{9} e^{x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{\frac{( 7 + 37 ) x}{2}} + c_{2} e^{\frac{( 7 - 37 ) x}{2}} - \frac{e ^{x} x}{3} + \frac{5}{9} e^{x}

y = c_{1} e^{\frac{( 7 + 37 ) x}{2}} + c_{2} e^{\frac{( 7 - 37 ) x}{2}} - \frac{e ^{x} x}{3} + \frac{5}{9} e^{x}

x \to 0 lim (\frac{5 x ^{2} - 4 x}{x})

k = 1 \sum \infty \frac{k !}{10 1 ^{k}}

d er i v a t i v e f (x) = 4 x^{2} - 5 x

\int 3 2 x + 10 d x

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