Internal problem ID [1983]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 9, page 38
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {x^{2} y^{2}-y+\left (2 y x^{3}+x \right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (2\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 20
dsolve([(x^2*y(x)^2-y(x))+(2*x^3*y(x)+x)*diff(y(x),x)=0,y(2) = -2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {-1-\sqrt {28 x^{3}+1}}{2 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.648 (sec). Leaf size: 34
DSolve[{(x^2*y[x]^2-y[x])+(2*x^3*y[x]+x)*y'[x]==0,{y[2]==-2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sqrt {\frac {1}{x^2}} \sqrt {28 x^3+1} x+1}{2 x^2} \]