x^2(dy)/(dx)=sqrt(y)(6x+4)

Lösung

x^{2} \frac{d y}{d x} = y (6 x + 4)

y = - \frac{2 c _{1}}{x} - \frac{12 ln ( x )}{x} + 3 c_{1} ln (x) + \frac{c _{1}^{2}}{4} + \frac{4}{x ^{2}} + 9 ln^{2} (x)

Schritte zur Lösung

x^{2} \frac{d y}{d x} = y (6 x + 4)

Solve separable ODE:

y = - \frac{2 c _{1}}{x} - \frac{12 ln ( x )}{x} + 3 c_{1} ln (x) + \frac{c _{1}^{2}}{4} + \frac{4}{x ^{2}} + 9 ln^{2} (x)

y = - \frac{2 c _{1}}{x} - \frac{12 ln ( x )}{x} + 3 c_{1} ln (x) + \frac{c _{1}^{2}}{4} + \frac{4}{x ^{2}} + 9 ln^{2} (x)

d x = A (cos (y) d x + x sin (y) d y)

(ln (y))^{4} \frac{d y}{d x} = x^{4} y

\frac{d y}{d x} + 15 x^{2} y = 15 x^{2}

\frac{d y}{d x} = (y + 1) (x + 1) cos (x^{2} + 2 x), y (0) = 4

y^{^{'}} + 2 (x + 1) y^{2} = 0