28.1.119 problem 142

Internal problem ID [4425]
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 : 142
Date solved : Monday, January 27, 2025 at 09:16:52 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x^{2}+3 \ln \left (y\right )-\frac {x y^{\prime }}{y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 14

dsolve((x^2+3*ln(y(x)))-x/y(x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{x^{2} \left (c_{1} x -1\right )} \]

✓ Solution by Mathematica

Time used: 0.267 (sec). Leaf size: 18

DSolve[(x^2+3*Log[y[x]])-x/y[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x^2 (-1+6 c_1 x)} \]