Internal problem ID [3955]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 9
Problem number: Exact Differential equations. Exercise 9.12, page 79.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _dAlembert]
Solve \begin {gather*} \boxed {x \sqrt {x^{2}+y^{2}}-\frac {x^{2} y y^{\prime }}{y-\sqrt {x^{2}+y^{2}}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 19
dsolve(x*sqrt(x^2+y(x)^2)-(x^2*y(x))/(y(x)- sqrt(x^2+y(x)^2))*diff(y(x),x)=0,y(x), singsol=all)
\[ c_{1}+\left (x^{2}+y \relax (x )^{2}\right )^{\frac {3}{2}}+y \relax (x )^{3} = 0 \]
✓ Solution by Mathematica
Time used: 0.915 (sec). Leaf size: 7585
DSolve[x*Sqrt[x^2+y[x]^2]-(x^2*y[x])/(y[x]- Sqrt[x^2+y[x]^2])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
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