29.36.2 problem 1065

Internal problem ID [5629]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1065
Date solved : Monday, January 27, 2025 at 12:32:03 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: 0.275 (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 \left (x \right ) &= \frac {3 \,2^{{1}/{3}} \left (-x \right )^{{1}/{3}}}{2} \\ y \left (x \right ) &= -\frac {3 \,2^{{1}/{3}} \left (-x \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{4} \\ y \left (x \right ) &= \frac {3 \,2^{{1}/{3}} \left (-x \right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{4} \\ y \left (x \right ) &= c_{1} x -\frac {1}{\sqrt {-c_{1}}} \\ y \left (x \right ) &= c_{1} x +\frac {1}{\sqrt {-c_{1}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 69.994 (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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