73.6.2 problem 7.2 (c)

Internal problem ID [15141]
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)
Date solved : Tuesday, January 28, 2025 at 07:36:35 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.034 (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 &= \frac {\sqrt {x \left (x^{2}-c_{1} \right )}}{x} \\ y &= -\frac {\sqrt {x \left (x^{2}-c_{1} \right )}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.116 (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]*D[y[x],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*}