60.1.240 problem 241

Internal problem ID [10254]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 241
Date solved : Monday, January 27, 2025 at 06:41:51 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.388 (sec). Leaf size: 37

DSolve[2*x*y[x]*D[y[x],x]-y[x]^2+a*x^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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