29.35.28 problem 1062

Internal problem ID [5626]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1062
Date solved : Monday, January 27, 2025 at 12:31:59 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Solution by Maple

Time used: 0.340 (sec). Leaf size: 77

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

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

✓ Solution by Mathematica

Time used: 99.868 (sec). Leaf size: 18492

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

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