53.3.26 problem 29

Internal problem ID [8488]
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 : 29
Date solved : Monday, January 27, 2025 at 04:07:15 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 105.496 (sec). Leaf size: 7052

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

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