Internal problem ID [2586]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition,
2000
Section: 1.8, page 68
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y^{\prime }-\frac {x \sqrt {y^{2}+x^{2}}+y^{2}}{y x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(diff(y(x),x)=(x*sqrt(x^2+y(x)^2)+y(x)^2)/(x*y(x)),y(x), singsol=all)
\[ \frac {x \ln \left (x \right )-c_{1} x -\sqrt {x^{2}+y \left (x \right )^{2}}}{x} = 0 \]
✓ Solution by Mathematica
Time used: 0.283 (sec). Leaf size: 54
DSolve[y'[x]==(x*Sqrt[x^2+y[x]^2]+y[x]^2)/(x*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {\log ^2(x)+2 c_1 \log (x)-1+c_1{}^2} \\ y(x)\to x \sqrt {\log ^2(x)+2 c_1 \log (x)-1+c_1{}^2} \\ \end{align*}