29.25.28 problem 725

Internal problem ID [5315]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 725
Date solved : Monday, January 27, 2025 at 11:08:53 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y^{\prime } \sqrt {y x}+x -y&=\sqrt {y x} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 84

dsolve(diff(y(x),x)*sqrt(x*y(x))+x-y(x) = sqrt(x*y(x)),y(x), singsol=all)
 

\[ \frac {\left (3 x -3 \sqrt {x y \left (x \right )}\right ) \ln \left (\sqrt {x y \left (x \right )}-x \right )+\left (-\sqrt {x y \left (x \right )}+x \right ) \ln \left (x +\sqrt {x y \left (x \right )}\right )+\left (2 \ln \left (x \right )+c_{1} \right ) \sqrt {x y \left (x \right )}-x \left (c_{1} +2 \ln \left (x \right )-2\right )}{-\sqrt {x y \left (x \right )}+x} = 0 \]

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 62

DSolve[D[y[x],x]*Sqrt[x*y[x]]+x -y[x]==Sqrt[x*y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\frac {1}{\sqrt {\frac {y(x)}{x}}-1}+\frac {3}{2} \log \left (\sqrt {\frac {y(x)}{x}}-1\right )+\frac {1}{2} \log \left (\sqrt {\frac {y(x)}{x}}+1\right )=-\log (x)+c_1,y(x)\right ] \]