53.3.3 problem 5

Internal problem ID [8465]
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 : 5
Date solved : Monday, January 27, 2025 at 04:04:23 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} 2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.472 (sec). Leaf size: 54

dsolve(2*x*diff(y(x),x)^3-6*y(x)*diff(y(x),x)^2+x^4=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {\left (1+i \sqrt {3}\right ) x^{2}}{4} \\ y &= \frac {\left (i \sqrt {3}-1\right ) x^{2}}{4} \\ y &= \frac {x^{2}}{2} \\ y &= \frac {1}{6 c_{1}^{2}}+\frac {c_{1} x^{3}}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 152.887 (sec). Leaf size: 21360

DSolve[2*x*(D[y[x],x])^3-6*y[x]*(D[y[x],x])^2+x^4==0,y[x],x,IncludeSingularSolutions -> True]
 

Too large to display