60.1.478 problem 481

Internal problem ID [10492]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 481
Date solved : Monday, January 27, 2025 at 08:15:05 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 35

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

\begin{align*} y &= \frac {c_{1}}{x} \\ y &= \sqrt {-x^{2}+c_{1}} \\ y &= -\sqrt {-x^{2}+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 54

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

\begin{align*} y(x)\to \frac {c_1}{x} \\ y(x)\to -\sqrt {-x^2+2 c_1} \\ y(x)\to \sqrt {-x^2+2 c_1} \\ y(x)\to 0 \\ \end{align*}