x^2y^{''}+2xy^'-12y=0,y(1)=-1,y^'(1)=10

Lösung

x^{2} y^{^{''}} + 2 x y^{^{'}} - 12 y = 0, y (1) = - 1, y^{^{'}} (1) = 10

y = (- 1 + \frac{13}{7}) x^{3} - \frac{13}{7 x ^{4}}

Schritte zur Lösung

x^{2} y^{''} (x) + 2 x y^{'} (x) - 12 y = 0

Solve linear ODE:

y = (- 1 + \frac{13}{7}) x^{3} - \frac{13}{7 x ^{4}}

y = (- 1 + \frac{13}{7}) x^{3} - \frac{13}{7 x ^{4}}

\frac{d x}{d y} = - \frac{4 y ^{2} + 6 x y}{3 y ^{2} + 2 x}

x \to 2 lim (x^{4})

d er i v a t i v e f (x) = \frac{2}{x - 3}

s l o p e y = 1 - x^{2}, at x = \frac{1}{2}

x \to 9 lim (\frac{( 16 + x )}{16 + x})