Internal problem ID [11611]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {3 y^{2}+2 x y y^{\prime }=-4 x} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) &= \frac {\sqrt {x \left (-x^{4}+c_{1} \right )}}{x^{2}} \\ y \left (x \right ) &= -\frac {\sqrt {x \left (-x^{4}+c_{1} \right )}}{x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.349 (sec). Leaf size: 46
DSolve[(4*x+3*y[x]^2)+(2*x*y[x])*y'[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*}