29.35.29 problem 1063

Internal problem ID [5627]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1063
Date solved : Monday, January 27, 2025 at 12:32:00 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Solution by Maple

Time used: 0.199 (sec). Leaf size: 84

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

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

✓ Solution by Mathematica

Time used: 1.070 (sec). Leaf size: 79

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

\begin{align*} y(x)\to -\frac {\sqrt {2} \sqrt {c_1 (x+c_1){}^3}+c_1{}^2}{3 c_1} \\ y(x)\to -\frac {c_1{}^2-\sqrt {2} \sqrt {c_1 (x+c_1){}^3}}{3 c_1} \\ y(x)\to \text {Indeterminate} \\ \end{align*}