Internal problem ID [925]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number: 48(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(y)]]]
Solve \begin {gather*} \boxed {{\mathrm e}^{y^{2}} \left (2 y y^{\prime }+\frac {2}{x}\right )-\frac {1}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve(exp(y(x)^2)*(2*y(x)*diff(y(x),x)+2/x)= 1/x^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {\ln \left (-\frac {c_{1}-x}{x^{2}}\right )} \\ y \relax (x ) = -\sqrt {\ln \left (-\frac {c_{1}-x}{x^{2}}\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.106 (sec). Leaf size: 37
DSolve[Exp[y[x]^2]*(2*y[x]*y'[x]+2/x)== 1/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {\log \left (\frac {x+c_1}{x^2}\right )} \\ y(x)\to \sqrt {\log \left (\frac {x+c_1}{x^2}\right )} \\ \end{align*}