Internal problem ID [2350]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 38, page 173
Problem number: 13.
ODE order: 1.
ODE degree: 4.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
\[ \boxed {3 {y^{\prime }}^{4} x -{y^{\prime }}^{3} y=1} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 37
dsolve(3*diff(y(x),x)^4*x=diff(y(x),x)^3*y(x)+1,y(x), singsol=all)
\[ \left [x \left (\textit {\_T} \right ) = \frac {\frac {3}{5 \textit {\_T}^{\frac {5}{2}}}+c_{1}}{\textit {\_T}^{\frac {3}{2}}}, y \left (\textit {\_T} \right ) = \frac {\frac {9}{5 \textit {\_T}^{\frac {5}{2}}}+3 c_{1}}{\sqrt {\textit {\_T}}}-\frac {1}{\textit {\_T}^{3}}\right ] \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[3*y'[x]^4*x==y'[x]^3*y[x]+1,y[x],x,IncludeSingularSolutions -> True]
Timed out