64.3.16 problem 21

Internal problem ID [13287]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 05:15:58 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 4 x +3 y^{2}+2 x y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 38

dsolve((4*x+3*y(x)^2)+(2*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.235 (sec). Leaf size: 46

DSolve[(4*x+3*y[x]^2)+(2*x*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {-x^4+c_1}}{x^{3/2}} \\ y(x)\to \frac {\sqrt {-x^4+c_1}}{x^{3/2}} \\ \end{align*}