x^2y^{''}+3xy^'=2

Lösung

x^{2} y^{^{''}} + 3 x y^{^{'}} = 2

y = c_{1} + \frac{c _{2}}{x ^{2}} + ln (x) - \frac{1}{2}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + \frac{c _{2}}{x ^{2}} + ln (x) - \frac{1}{2}

y = c_{1} + \frac{c _{2}}{x ^{2}} + ln (x) - \frac{1}{2}

\frac{d}{d x} (ln (8 x^{2} + 7 x + 2))

\int_{1}^{3} \frac{7}{16 - x ^{2}} d x

\int \frac{26 x ^{3} - 52 x ^{2} + 7}{x ^{2} - 2 x} d x

d er i v a t i v e ln (9)

\int_{0}^{1} \frac{x}{( x ^{2} + 1 ) ^{3}} d x