(d^2-d-2)y=2log_{10}(x)+1/x+1/((x^2))

Lösung

(d^{2} - d - 2) \cdot y = 2 \cdot lo g_{10} (x) + \frac{1}{x} + \frac{1}{( x ^{2} )}

y = c_{1} e^{2 x} + c_{2} e^{- x} + e^{2 x} \cdot \int \frac{2 x ^{2} lo g _{10} ( x ) + x + 1}{3 e ^{2 x} x ^{2}} d x - \frac{1}{3} e^{- x} (\frac{( - 2 + 2 ln ( 10 ) ) Ei ( x )}{ln ( 10 )} + 2 e^{x} lo g_{10} (x) - \frac{e ^{x}}{x})

Schritte zur Lösung

(d^{2} - d - 2) y = 2 lo g_{10} (x) + \frac{1}{x} + \frac{1}{x ^{2}}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} + e^{2 x} \cdot \int \frac{2 x ^{2} lo g _{10} ( x ) + x + 1}{3 e ^{2 x} x ^{2}} d x - \frac{1}{3} e^{- x} (\frac{( - 2 + 2 ln ( 10 ) ) Ei ( x )}{ln ( 10 )} + 2 e^{x} lo g_{10} (x) - \frac{e ^{x}}{x})

y = c_{1} e^{2 x} + c_{2} e^{- x} + e^{2 x} \cdot \int \frac{2 x ^{2} lo g _{10} ( x ) + x + 1}{3 e ^{2 x} x ^{2}} d x - \frac{1}{3} e^{- x} (\frac{( - 2 + 2 ln ( 10 ) ) Ei ( x )}{ln ( 10 )} + 2 e^{x} lo g_{10} (x) - \frac{e ^{x}}{x})

(d - 5)^{2} y = e^{5 x}

(d^{2} - 5 d + 6) \cdot y = x

y^{^{''}} - 6 y^{^{'}} + 8 y = 16 x^{2} - 2

(d^{3} - 2 d^{2} - 5 d + 6) y = e^{4} x

(d^{3} - 4 d) y = 2 cosh^{2} (2 x)