62.12.29 problem Ex 30

Internal problem ID [12875]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number : Ex 30
Date solved : Tuesday, January 28, 2025 at 04:29:59 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} \left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 18

dsolve((2*sqrt(x*y(x))-x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.264 (sec). Leaf size: 33

DSolve[(2*Sqrt[x*y[x]]-x)*D[y[x],x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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