Internal problem ID [10185]
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 19. Summary.
Page 29
Problem number: Ex 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {\left (2 \sqrt {y x}-x \right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve((2*sqrt(x*y(x))-x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ \ln \left (y \relax (x )\right )+\frac {x}{\sqrt {x y \relax (x )}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.24 (sec). Leaf size: 33
DSolve[(2*Sqrt[x*y[x]]-x)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2}{\sqrt {\frac {y(x)}{x}}}+2 \log \left (\frac {y(x)}{x}\right )=-2 \log (x)+c_1,y(x)\right ] \]