Internal problem ID [12499]
Internal file name [OUTPUT/11152_Monday_October_16_2023_09_54_06_PM_48316860/index.tex]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 128.
ODE order: 2.
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_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)^2-2*(diff(_b(_a), _a))^2*_b(_a) = 0, _b(_a), HINT = [[_a, _b], symmetry methods on request `, `2nd order, trying reduction of order with given symmetries:`[_a, _b], [1, 0], [0, _b^2], [0, _b]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 59
dsolve(diff(y(x),x)*diff(y(x),x$3)-3*diff(y(x),x$2)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= c_{1} \\ y \left (x \right ) &= \frac {-c_{1} c_{2} +\sqrt {-2 \left (-\frac {c_{1} c_{2}^{2}}{2}+x +c_{3} \right ) c_{1}}}{c_{1}} \\ y \left (x \right ) &= \frac {-c_{1} c_{2} -\sqrt {-2 \left (-\frac {c_{1} c_{2}^{2}}{2}+x +c_{3} \right ) c_{1}}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.307 (sec). Leaf size: 21
DSolve[y'[x]*y'''[x]-3*(y''[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 \sqrt {2 x+c_1}+c_3 \]