Internal problem ID [13405]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 7. The exact form and general integrating fators. Additional exercises. page
141
Problem number: 7.2 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]
\[ \boxed {{\mathrm e}^{y^{2} x -x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{y^{2} x -x^{2}} x y y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 38
dsolve(exp(x*y(x)^2-x^2)*(y(x)^2-2*x)+exp(x*y(x)^2-x^2)*2*x*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {x \left (x^{2}-c_{1} \right )}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {x \left (x^{2}-c_{1} \right )}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.12 (sec). Leaf size: 42
DSolve[Exp[x*y[x]^2-x^2]*(y[x]^2-2*x)+Exp[x*y[x]^2-x^2]*2*x*y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x^2+c_1}}{\sqrt {x}} \\ y(x)\to \frac {\sqrt {x^2+c_1}}{\sqrt {x}} \\ \end{align*}