60.1.239 problem 240

Internal problem ID [10253]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 240
Date solved : Monday, January 27, 2025 at 06:41:50 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 2 x y y^{\prime }-y^{2}+a x&=0 \end{align*}

Solution by Maple

Time used: 0.013 (sec). Leaf size: 35

dsolve(2*x*y(x)*diff(y(x),x)-y(x)^2+a*x=0,y(x), singsol=all)
 
\begin{align*} y &= \sqrt {-x \left (a \ln \left (x \right )-c_{1} \right )} \\ y &= -\sqrt {-x \left (a \ln \left (x \right )-c_{1} \right )} \\ \end{align*}

Solution by Mathematica

Time used: 0.430 (sec). Leaf size: 39

DSolve[2*x*y[x]*D[y[x],x]-y[x]^2+a*x==0,y[x],x,IncludeSingularSolutions -> True]
 
\begin{align*} y(x)\to -\sqrt {x (-a \log (x)+c_1)} \\ y(x)\to \sqrt {x (-a \log (x)+c_1)} \\ \end{align*}