Internal problem ID [5858]
Internal file name [OUTPUT/5106_Sunday_June_05_2022_03_24_49_PM_35055999/index.tex]
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.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode 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]]
Unable to solve or complete the solution.
Unable to parse ODE.
Maple trace
`Methods for third order ODEs: --- Trying classification methods --- trying 3rd order ODE linearizable_by_differentiation differential order: 3; trying a linearization to 4th order trying differential order: 3; missing variables `, `-> Computing symmetries using: way = 3 -> Calling odsolve with the ODE`, (diff(diff(_b(_a), _a), _a))*_b(_a)^2-(diff(_b(_a), _a))*_b(_a)*(2*(diff(_b(_a), _a))-_b(_a)) = 0, symmetry methods on request `, `2nd order, trying reduction of order with given symmetries:`[0, _b^2], [1, 0], [0, _b]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 38
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 \left (x \right ) &= c_{1} \\ y \left (x \right ) &= \frac {\operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {c_{3} +x}{c_{1}}}}{c_{2} c_{1}}\right ) c_{1} -c_{3} -x}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.622 (sec). Leaf size: 79
DSolve[3*(y''[x])^2-y'[x]*y'''[x]-y''[x]*(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \log \left (\text {InverseFunction}\left [-\frac {1}{\text {$\#$1}}-c_1 \log (\text {$\#$1})+c_1 \log (1+\text {$\#$1} c_1)\&\right ][x+c_2]\right )-\log \left (1+c_1 \text {InverseFunction}\left [-\frac {1}{\text {$\#$1}}-c_1 \log (\text {$\#$1})+c_1 \log (1+\text {$\#$1} c_1)\&\right ][x+c_2]\right )+c_3 \]