73.6.6 problem 7.4 (d)

Internal problem ID [15145]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 7. The exact form and general integrating fators. Additional exercises. page 141
Problem number : 7.4 (d)
Date solved : Tuesday, January 28, 2025 at 07:36:48 AM
CAS classification : [_exact, _rational, _Bernoulli]

\begin{align*} 1+3 x^{2} y^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

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

dsolve(1+3*x^2*y(x)^2+(2*x^3*y(x)+6*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {\sqrt {\left (x^{3}+3\right ) \left (-x +c_{1} \right )}}{x^{3}+3} \\ y &= -\frac {\sqrt {\left (x^{3}+3\right ) \left (-x +c_{1} \right )}}{x^{3}+3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.235 (sec). Leaf size: 50

DSolve[1+3*x^2*y[x]^2+(2*x^3*y[x]+6*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {-x+c_1}}{\sqrt {x^3+3}} \\ y(x)\to \frac {\sqrt {-x+c_1}}{\sqrt {x^3+3}} \\ \end{align*}