54.2.10 problem 11

Internal problem ID [8542]
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
Date solved : Monday, January 27, 2025 at 04:13:22 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} {y^{\prime }}^{4}+x y^{\prime }-3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 34

dsolve(diff(y(x),x)^4+x*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
 

\[ \left [x \left (\textit {\_T} \right ) = \frac {\sqrt {\textit {\_T}}\, \left (4 \textit {\_T}^{{5}/{2}}+5 c_{1} \right )}{5}, y \left (\textit {\_T} \right ) = \frac {3 \textit {\_T}^{4}}{5}+\frac {\textit {\_T}^{{3}/{2}} c_{1}}{3}\right ] \]

✗ Solution by Mathematica

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

DSolve[(D[y[x],x])^4+x*D[y[x],x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Timed out