Internal problem ID [3169]
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)]`]]
\[ \boxed {\ln \left (y\right )=-x^{2}-\frac {x y^{\prime }}{y}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve((x^2+ln(y(x)))+(x/y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {x^{3}+3 c_{1}}{3 x}} \]
✓ Solution by Mathematica
Time used: 0.247 (sec). Leaf size: 21
DSolve[(x^2+Log[y[x]])+(x/y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-\frac {x^2}{3}+\frac {c_1}{x}} \]