81.3.21 problem 21

Internal problem ID [18639]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 12:05:15 PM
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: 0.006 (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: 0.254 (sec). Leaf size: 21

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

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