Internal problem ID [6119]
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.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {4 x^{5} \left (y^{\prime }\right )^{2}+12 x^{4} y y^{\prime }+9=0} \end {gather*}
✓ Solution by Maple
Time used: 0.531 (sec). Leaf size: 47
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 \relax (x ) = \frac {x^{3} c_{1}^{2}+1}{2 c_{1} x^{3}} \\ y \relax (x ) = \frac {x^{3}+c_{1}^{2}}{2 c_{1} x^{3}} \\ y \relax (x ) = \frac {c_{1}}{x^{\frac {3}{2}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 10.925 (sec). Leaf size: 75
DSolve[4*x^5*(y'[x])^2+12*x^4*y[x]*y'[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*}