53.3.21 problem 24

Internal problem ID [8483]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 99. Clairaut equation. EXERCISES Page 320
Problem number : 24
Date solved : Monday, January 27, 2025 at 04:07:10 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} {y^{\prime }}^{3}-x y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 58

dsolve(diff(y(x),x)^3-x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {\left (c_{1}^{2}-12 x \right )^{{3}/{2}}}{108}-\frac {c_{1}^{3}}{108}+\frac {c_{1} x}{6} \\ y &= \frac {\left (-c_{1}^{2}+12 x \right ) \sqrt {c_{1}^{2}-12 x}}{108}-\frac {c_{1}^{3}}{108}+\frac {c_{1} x}{6} \\ \end{align*}

✓ Solution by Mathematica

Time used: 158.124 (sec). Leaf size: 10134

DSolve[(D[y[x],x])^3-x*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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