Internal problem ID [6037]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 97. The p-discriminant equation. EXERCISES
Page 314
Problem number: 12.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+4 y^{\prime } x^{5}-12 y x^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.844 (sec). Leaf size: 23
dsolve(diff(y(x),x)^2+4*x^5*diff(y(x),x)-12*x^4*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {x^{6}}{3} \\ y \relax (x ) = x^{3} c_{1}+\frac {3}{4} c_{1}^{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.046 (sec). Leaf size: 217
DSolve[(y'[x])^2+4*x^5*y'[x]-12*x^4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\frac {1}{6} \left (\log (y(x))-\frac {x^2 \sqrt {x^6+3 y(x)} \log (y(x))}{\sqrt {x^4 \left (x^6+3 y(x)\right )}}\right )+\frac {x^2 \sqrt {x^6+3 y(x)} \log \left (\sqrt {x^6+3 y(x)}+x^3\right )}{3 \sqrt {x^4 \left (x^6+3 y(x)\right )}}=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {1}{6} \left (\frac {x^2 \sqrt {x^6+3 y(x)} \log (y(x))}{\sqrt {x^4 \left (x^6+3 y(x)\right )}}+\log (y(x))\right )-\frac {x^2 \sqrt {x^6+3 y(x)} \log \left (\sqrt {x^6+3 y(x)}+x^3\right )}{3 \sqrt {x^4 \left (x^6+3 y(x)\right )}}=c_1,y(x)\right ] \\ y(x)\to -\frac {x^6}{3} \\ \end{align*}