54.2.11 problem 13

Internal problem ID [8543]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number : 13
Date solved : Monday, January 27, 2025 at 04:13:25 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.060 (sec). Leaf size: 80

dsolve(x^2*diff(y(x),x)^3-2*x*y(x)*diff(y(x),x)^2+y(x)^2*diff(y(x),x)+1=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 136.313 (sec). Leaf size: 33909

DSolve[x^2*(D[y[x],x])^3-2*x*y[x]*(D[y[x],x])^2+y[x]^2*D[y[x],x]+1==0,y[x],x,IncludeSingularSolutions -> True]
 

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