Internal problem ID [5105]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page
181
Problem number: Example 3.30.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]
Solve \begin {gather*} \boxed {3 \left (y^{\prime \prime }\right )^{2}-y^{\prime } y^{\prime \prime \prime }-y^{\prime \prime } \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.19 (sec). Leaf size: 42
dsolve(3*diff(y(x),x$2)^2-diff(y(x),x)*diff(y(x),x$3)-diff(y(x),x$2)*diff(y(x),x)^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} \\ y \relax (x ) = \frac {\LambertW \left (-\frac {{\mathrm e}^{\frac {c_{3}}{c_{1}}} {\mathrm e}^{\frac {x}{c_{1}}}}{c_{2} c_{1}}\right ) c_{1}-c_{3}-x}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.164 (sec). Leaf size: 79
DSolve[3*(y''[x])^2-y'[x]*y'''[x]-y''[x]*(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (\text {InverseFunction}\left [-\frac {1}{\text {$\#$1}}-c_1 \log (\text {$\#$1})+c_1 \log (1+\text {$\#$1} c_1)\&\right ][x+c_2]\right )-\log \left (1+c_1 \text {InverseFunction}\left [-\frac {1}{\text {$\#$1}}-c_1 \log (\text {$\#$1})+c_1 \log (1+\text {$\#$1} c_1)\&\right ][x+c_2]\right )+c_3 \\ \end{align*}