54.2.8 problem 9

Internal problem ID [8540]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number : 9
Date solved : Monday, January 27, 2025 at 04:11:28 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \end{align*}

✓ Solution by Maple

Time used: 0.171 (sec). Leaf size: 53

dsolve(4*x^5*diff(y(x),x)^2+12*x^4*y(x)*diff(y(x),x)+9=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {1}{x^{{3}/{2}}} \\ y &= -\frac {1}{x^{{3}/{2}}} \\ y &= \frac {c_{1}^{2} x^{3}+1}{2 c_{1} x^{3}} \\ y &= \frac {x^{3}+c_{1}^{2}}{2 c_{1} x^{3}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 6.198 (sec). Leaf size: 75

DSolve[4*x^5*(D[y[x],x])^2+12*x^4*y[x]*D[y[x],x]+9==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\sqrt {x^3 \text {sech}^2\left (\frac {3}{2} (-\log (x)+c_1)\right )}} \\ y(x)\to \frac {1}{\sqrt {x^3 \text {sech}^2\left (\frac {3}{2} (-\log (x)+c_1)\right )}} \\ y(x)\to -\frac {1}{x^{3/2}} \\ y(x)\to \frac {1}{x^{3/2}} \\ \end{align*}