Internal problem ID [2660]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]
Solve \begin {gather*} \boxed {x^{2}+\ln \relax (y)+\frac {x y^{\prime }}{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 19
dsolve((x^2+ln(y(x)))+(x/y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x^{2}}{3}} {\mathrm e}^{-\frac {c_{1}}{x}} \]
✓ Solution by Mathematica
Time used: 0.235 (sec). Leaf size: 21
DSolve[(x^2+Log[y[x]])+(x/y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\frac {x^2}{3}+\frac {c_1}{x}} \\ \end{align*}