15.20.13 problem 13

Internal problem ID [3321]
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
Date solved : Monday, January 27, 2025 at 07:33:35 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} 3 {y^{\prime }}^{4} x&={y^{\prime }}^{3} y+1 \end{align*}

Solution by Maple

Time used: 0.042 (sec). Leaf size: 34

dsolve(3*diff(y(x),x)^4*x=diff(y(x),x)^3*y(x)+1,y(x), singsol=all)
 
\[ \left [x \left (\textit {\_T} \right ) = \frac {5 c_{1} \textit {\_T}^{{5}/{2}}+3}{5 \textit {\_T}^{4}}, y \left (\textit {\_T} \right ) = \frac {15 c_{1} \textit {\_T}^{{5}/{2}}+4}{5 \textit {\_T}^{3}}\right ] \]

Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[3*D[y[x],x]^4*x==D[y[x],x]^3*y[x]+1,y[x],x,IncludeSingularSolutions -> True]
 

Timed out