62.9.5 problem Ex 5

Internal problem ID [12836]
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 16. Integrating factors by inspection. Page 23
Problem number : Ex 5
Date solved : Tuesday, January 28, 2025 at 04:26:16 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x -y^{2}+2 x y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 30

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

\begin{align*} y &= \sqrt {-x \left (\ln \left (x \right )-c_{1} \right )} \\ y &= -\sqrt {\left (-\ln \left (x \right )+c_{1} \right ) x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.194 (sec). Leaf size: 44

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

\begin{align*} y(x)\to -\sqrt {x} \sqrt {-\log (x)+c_1} \\ y(x)\to \sqrt {x} \sqrt {-\log (x)+c_1} \\ \end{align*}