y^{''}-2/x y^'-4/(x^2)y=3x^2

Lösung

y^{^{''}} - \frac{2}{x} y^{^{'}} - \frac{4}{x ^{2}} y = 3 x^{2}

y = c_{1} x^{4} + \frac{c _{2}}{x} + \frac{3}{5} x^{4} ln (x) - \frac{3 x ^{4}}{25}

Schritte zur Lösung

y^{''} (x) - \frac{2}{x} y^{'} (x) - \frac{4}{x ^{2}} y = 3 x^{2}

Solve linear ODE:

y = c_{1} x^{4} + \frac{c _{2}}{x} + \frac{3}{5} x^{4} ln (x) - \frac{3 x ^{4}}{25}

y = c_{1} x^{4} + \frac{c _{2}}{x} + \frac{3}{5} x^{4} ln (x) - \frac{3 x ^{4}}{25}

x \to 1 + lim (x^{3} - 4)

x \to - 1 lim (\frac{2 x}{x + 1})

n = 1 \sum \infty \frac{3}{n ^{4}}

h \to 0 lim (\frac{( 1 + h ) ^{2} - 1}{h})

x \to 1 lim (1 + 6 x^{2})