73.7.12 problem 12

Internal problem ID [15170]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 07:39:54 AM
CAS classification : [_exact, _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 50

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

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

✓ Solution by Mathematica

Time used: 0.232 (sec). Leaf size: 50

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

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