Internal problem ID [6067]
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]
Solve \begin {gather*} \boxed {y-x y^{\prime }-x^{3} \left (y^{\prime }\right )^{2}=0} \end {gather*}
✗ 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: 105.827 (sec). Leaf size: 7052
DSolve[y[x]==x*y'[x]+x^3*(y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
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