Internal problem ID [6865]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th
edition. 1997.
Section: CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number: 1.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }=-4} \]
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 53
dsolve(x^3*diff(y(x),x)^2+x^2*y(x)*diff(y(x),x)+4=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {4}{\sqrt {x}} y \left (x \right ) = \frac {4}{\sqrt {x}} y \left (x \right ) = \frac {x \,c_{1}^{2}+16}{2 x c_{1}} y \left (x \right ) = \frac {c_{1}^{2}+16 x}{2 x c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.558 (sec). Leaf size: 77
DSolve[x^3*(y'[x])^2+x^2*y[x]*y'[x]+4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{-\frac {c_1}{2}} \left (x+64 e^{c_1}\right )}{4 x} y(x)\to \frac {e^{-\frac {c_1}{2}} \left (x+64 e^{c_1}\right )}{4 x} y(x)\to -\frac {4}{\sqrt {x}} y(x)\to \frac {4}{\sqrt {x}} \end{align*}