Internal problem ID [13146]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 44.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y^{2} {\mathrm e}^{y^{2} x}+2 x y \,{\mathrm e}^{y^{2} x} y^{\prime }=2 x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 40
dsolve(y(x)^2*exp(x*y(x)^2)-2*x+2*x*y(x)*exp(x*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\sqrt {x \ln \left (x^{2}-c_{1} \right )}}{x} y \left (x \right ) = -\frac {\sqrt {x \ln \left (x^{2}-c_{1} \right )}}{x} \end{align*}
✓ Solution by Mathematica
Time used: 1.468 (sec). Leaf size: 44
DSolve[y[x]^2*Exp[x*y[x]^2]-2*x+2*x*y[x]*Exp[x*y[x]^2]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\log \left (x^2+c_1\right )}}{\sqrt {x}} y(x)\to \frac {\sqrt {\log \left (x^2+c_1\right )}}{\sqrt {x}} \end{align*}