3.26 problem 29

Internal problem ID [6820]

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’s equation. EXERCISES Page 320
Problem number: 29.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [[_homogeneous, `class G`], _rational]

\[ \boxed {y-x y^{\prime }-x^{3} {y^{\prime }}^{2}=0} \]

✗ 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: 105.562 (sec). Leaf size: 7052

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

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