28.1.24 problem 24

Internal problem ID [4330]
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
Date solved : Monday, January 27, 2025 at 09:03:25 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x^{2}+\ln \left (y\right )+\frac {x y^{\prime }}{y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.020 (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: 0.244 (sec). Leaf size: 21

DSolve[(x^2+Log[y[x]])+(x/y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-\frac {x^2}{3}+\frac {c_1}{x}} \]