60.1.331 problem 332

Internal problem ID [10345]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 332
Date solved : Monday, January 27, 2025 at 07:17:34 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} \left (\sqrt {y x}-1\right ) x y^{\prime }-\left (\sqrt {y x}+1\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ -\frac {1+\left (c_{1} -\ln \left (x \right )+\frac {\ln \left (x y\right )}{2}\right ) \sqrt {x y}}{\sqrt {x y}} = 0 \]

✓ Solution by Mathematica

Time used: 0.211 (sec). Leaf size: 29

DSolve[-(y[x]*(1 + Sqrt[x*y[x]])) + x*(-1 + Sqrt[x*y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {2}{\sqrt {x y(x)}}+2 \log (y(x))-\log (x y(x))=c_1,y(x)\right ] \]