60.1.336 problem 337

Internal problem ID [10350]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 337
Date solved : Monday, January 27, 2025 at 07:19:07 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.075 (sec). Leaf size: 27

dsolve(((y(x)^2+x^2)^(1/2)+x)*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
 

\[ \frac {-c_{1} y^{2}+\sqrt {x^{2}+y^{2}}+x}{y^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 0.515 (sec). Leaf size: 57

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

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