Internal problem ID [10110]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 8. Exact
differential equations. Page 11
Problem number: Ex 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, _dAlembert]
Solve \begin {gather*} \boxed {\frac {1}{\sqrt {y^{2}+x^{2}}}+\left (\frac {1}{y}-\frac {x}{y \sqrt {y^{2}+x^{2}}}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(1/sqrt(x^2+y(x)^2)+ ( 1/y(x)-(x/(y(x)*sqrt(x^2+y(x)^2))))*diff(y(x),x)=0,y(x), singsol=all)
\[ -c_{1}+\sqrt {x^{2}+y \relax (x )^{2}}+x = 0 \]
✓ Solution by Mathematica
Time used: 0.562 (sec). Leaf size: 62
DSolve[1/Sqrt[x^2+y[x]^2]+ ( 1/y[x]-(x/(y[x]*Sqrt[x^2+y[x]^2])))*y'[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 \\ y(x)\to \text {ComplexInfinity} \\ \end{align*}