53.4.37 problem 40

Internal problem ID [8525]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES Page 324
Problem number : 40
Date solved : Monday, January 27, 2025 at 04:09:19 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} {y^{\prime \prime }}^{2}-x y^{\prime \prime }+y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.190 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)^2-x*diff(y(x),x$2)+diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {x^{3}}{12}+c_{1} \\ y &= \frac {1}{2} c_{1} x^{2}-x \,c_{1}^{2}+c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 24

DSolve[(D[y[x],{x,2}])^2-x*D[y[x],{x,2}]+D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 x^2}{2}-c_1{}^2 x+c_2 \]