Internal problem ID [6874]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th
edition. 1997.
Section: CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number: 11.
ODE order: 1.
ODE degree: 4.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
\[ \boxed {{y^{\prime }}^{4}+x y^{\prime }-3 y=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 34
dsolve(diff(y(x),x)^4+x*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
\[ \left [x \left (\textit {\_T} \right ) = \frac {\sqrt {\textit {\_T}}\, \left (4 \textit {\_T}^{\frac {5}{2}}+5 c_{1} \right )}{5}, y \left (\textit {\_T} \right ) = \frac {3 \textit {\_T}^{4}}{5}+\frac {\textit {\_T}^{\frac {3}{2}} c_{1}}{3}\right ] \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y'[x])^4+x*y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out