54.2.1 problem 1

Internal problem ID [8533]
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
Date solved : Monday, January 27, 2025 at 04:09:47 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.137 (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 &= -\frac {4}{\sqrt {x}} \\ y &= \frac {4}{\sqrt {x}} \\ y &= \frac {c_{1}^{2} x +16}{2 c_{1} x} \\ y &= \frac {c_{1}^{2}+16 x}{2 c_{1} x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.760 (sec). Leaf size: 77

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

\begin{align*} y(x)\to -\frac {e^{-\frac {c_1}{2}} \left (x+16 e^{c_1}\right )}{2 x} \\ y(x)\to \frac {e^{-\frac {c_1}{2}} \left (x+16 e^{c_1}\right )}{2 x} \\ y(x)\to -\frac {4}{\sqrt {x}} \\ y(x)\to \frac {4}{\sqrt {x}} \\ \end{align*}