Internal problem ID [3971]
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]
\[ \boxed {y^{\prime } \sqrt {y x}-y-\sqrt {y x}=-x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 84
dsolve(diff(y(x),x)*sqrt(x*y(x))+x-y(x) = sqrt(x*y(x)),y(x), singsol=all)
\[ \frac {\left (3 x -3 \sqrt {x y \left (x \right )}\right ) \ln \left (-x +\sqrt {x y \left (x \right )}\right )+\left (x -\sqrt {x y \left (x \right )}\right ) \ln \left (\sqrt {x y \left (x \right )}+x \right )+\left (2 \ln \left (x \right )+c_{1} \right ) \sqrt {x y \left (x \right )}-x \left (c_{1} +2 \ln \left (x \right )-2\right )}{x -\sqrt {x y \left (x \right )}} = 0 \]
✓ Solution by Mathematica
Time used: 0.235 (sec). Leaf size: 62
DSolve[y'[x] Sqrt[x y[x]]+x -y[x]==Sqrt[x y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{1-\sqrt {\frac {y(x)}{x}}}+\frac {3}{2} \log \left (\sqrt {\frac {y(x)}{x}}-1\right )+\frac {1}{2} \log \left (\sqrt {\frac {y(x)}{x}}+1\right )=-\log (x)+c_1,y(x)\right ] \]