40.3.30 problem 26 (d)

Internal problem ID [6634]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 26 (d)
Date solved : Monday, January 27, 2025 at 02:16:25 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 37

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

\begin{align*} y &= \frac {c_1}{2}-\frac {\sqrt {c_1^{2}-4 x}}{2} \\ y &= \frac {c_1}{2}+\frac {\sqrt {c_1^{2}-4 x}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.271 (sec). Leaf size: 54

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

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