Internal problem ID [6121]
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]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{4}+x y^{\prime }-3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 37
dsolve(diff(y(x),x)^4+x*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
\[ \left [x \left (\textit {\_T} \right ) = \sqrt {\textit {\_T}}\, \left (\frac {4 \textit {\_T}^{\frac {5}{2}}}{5}+c_{1}\right ), y \left (\textit {\_T} \right ) = \frac {\textit {\_T}^{4}}{3}+\frac {\textit {\_T}^{\frac {3}{2}} \left (\frac {4 \textit {\_T}^{\frac {5}{2}}}{5}+c_{1}\right )}{3}\right ] \]
✗ 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