26.3.4 problem 4(a)

Internal problem ID [4264]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 10, page 47
Problem number : 4(a)
Date solved : Monday, January 27, 2025 at 08:46:57 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

\begin{align*} \left (x -1-y^{2}\right ) y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 39

dsolve((x-1-y(x)^2)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {c_{1}}{2}-\frac {\sqrt {c_{1}^{2}-4 x +4}}{2} \\ y \left (x \right ) &= \frac {c_{1}}{2}+\frac {\sqrt {c_{1}^{2}-4 x +4}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.285 (sec). Leaf size: 56

DSolve[(x-1-y[x]^2)*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (c_1-\sqrt {-4 x+4+c_1{}^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {-4 x+4+c_1{}^2}+c_1\right ) \\ y(x)\to 0 \\ \end{align*}