Internal problem ID [3463]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 725.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } \sqrt {y x}+x -y-\sqrt {y x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 48
dsolve(diff(y(x),x)*sqrt(x*y(x))+x-y(x) = sqrt(x*y(x)),y(x), singsol=all)
\[ 3 \ln \left (-x +\sqrt {x y \relax (x )}\right )-\frac {2 x}{-x +\sqrt {x y \relax (x )}}+\ln \left (\sqrt {x y \relax (x )}+x \right )-2 \ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.143 (sec). Leaf size: 62
DSolve[y'[x] Sqrt[x y[x]]+x -y[x]==Sqrt[x y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{1-\sqrt {\frac {y(x)}{x}}}+\frac {3}{2} \log \left (\sqrt {\frac {y(x)}{x}}-1\right )+\frac {1}{2} \log \left (\sqrt {\frac {y(x)}{x}}+1\right )=-\log (x)+c_1,y(x)\right ] \]