Internal problem ID [4283]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1063.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
\[ \boxed {4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+3 y=x} \]
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 102
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 ) = \left (-\frac {1}{2}-\frac {\sqrt {3}}{2}\right ) x y \left (x \right ) = \left (\frac {\sqrt {3}}{2}-\frac {1}{2}\right ) x y \left (x \right ) = x y \left (x \right ) = \frac {\left (\frac {\left (x +c_{1} \right ) \sqrt {2}\, \sqrt {c_{1} \left (x +c_{1} \right )}}{c_{1}^{2}}+1\right ) x}{-\frac {3 \left (x +c_{1} \right )}{c_{1}}+3} y \left (x \right ) = \frac {\left (-\frac {\left (x +c_{1} \right ) \sqrt {2}\, \sqrt {c_{1} \left (x +c_{1} \right )}}{c_{1}^{2}}+1\right ) x}{-\frac {3 \left (x +c_{1} \right )}{c_{1}}+3} \end{align*}
✓ Solution by Mathematica
Time used: 1.317 (sec). Leaf size: 79
DSolve[4 x (y'[x])^3 -6 y[x] (y'[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*}