76.5.30 problem 31

Internal problem ID [17450]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 10:38:41 AM
CAS classification : [_exact, _Bernoulli]

\begin{align*} 2 x y y^{\prime }+\ln \left (x \right )&=-y^{2}-1 \end{align*}

✓ Solution by Maple

Time used: 0.045 (sec). Leaf size: 42

dsolve(2*x*y(x)*diff(y(x),x)+ln(x)=-y(x)^2-1,y(x), singsol=all)
 

\begin{align*} y &= \frac {\sqrt {-x \left (\ln \left (x \right ) x -c_{1} \right )}}{x} \\ y &= -\frac {\sqrt {-x \left (\ln \left (x \right ) x -c_{1} \right )}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.217 (sec). Leaf size: 46

DSolve[2*x*y[x]*D[y[x],x]+Log[x]==-y[x]^2-1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {-x \log (x)+c_1}}{\sqrt {x}} \\ y(x)\to \frac {\sqrt {-x \log (x)+c_1}}{\sqrt {x}} \\ \end{align*}