Internal problem ID [8668]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 332.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {\left (\sqrt {y x}-1\right ) x y^{\prime }-\left (\sqrt {y x}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(((x*y(x))^(1/2)-1)*x*diff(y(x),x)-((x*y(x))^(1/2)+1)*y(x) = 0,y(x), singsol=all)
\[ -\frac {1+\left (c_{1} -\ln \left (x \right )+\frac {\ln \left (x y \left (x \right )\right )}{2}\right ) \sqrt {x y \left (x \right )}}{\sqrt {x y \left (x \right )}} = 0 \]
✓ Solution by Mathematica
Time used: 0.203 (sec). Leaf size: 29
DSolve[-(y[x]*(1 + Sqrt[x*y[x]])) + x*(-1 + Sqrt[x*y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2}{\sqrt {x y(x)}}+2 \log (y(x))-\log (x y(x))=c_1,y(x)\right ] \]