40.3.16 problem 25 (a)

Internal problem ID [6620]
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 : 25 (a)
Date solved : Monday, January 27, 2025 at 02:16:12 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 37

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

\begin{align*} y &= \sqrt {{\mathrm e}^{2 x} c_1 -x^{2}} \\ y &= -\sqrt {{\mathrm e}^{2 x} c_1 -x^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 4.928 (sec). Leaf size: 47

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

\begin{align*} y(x)\to -\sqrt {-x^2+c_1 e^{2 x}} \\ y(x)\to \sqrt {-x^2+c_1 e^{2 x}} \\ \end{align*}