75.7.14 problem 189

Internal problem ID [16807]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 7, Total differential equations. The integrating factor. Exercises page 61
Problem number : 189
Date solved : Tuesday, January 28, 2025 at 09:33:20 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class B`]]

\begin{align*} 1-x^{2} y+x^{2} \left (y-x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 51

dsolve(( 1-x^2*y(x))+x^2*(y(x)-x)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {x^{2}+\sqrt {x \left (x^{3}-2 c_{1} x +2\right )}}{x} \\ y &= \frac {x^{2}-\sqrt {x \left (x^{3}-2 c_{1} x +2\right )}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.587 (sec). Leaf size: 66

DSolve[( 1-x^2*y[x])+x^2*(y[x]-x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x+\sqrt {-\frac {1}{x^2}} \sqrt {-x \left (x^3+c_1 x+2\right )} \\ y(x)\to x-\sqrt {-\frac {1}{x^2}} \sqrt {-x \left (x^3+c_1 x+2\right )} \\ \end{align*}