Internal problem ID [7110]
Internal file name [OUTPUT/6096_Sunday_June_05_2022_04_21_39_PM_99630569/index.tex]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 66.
ODE order: 2.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[NONE]
Unable to solve or complete the solution.
\[ \boxed {3 y y^{\prime \prime }=\sin \left (x \right )} \]
Maple trace
`Methods for second order ODEs: --- Trying classification methods --- trying 2nd order Liouville trying 2nd order WeierstrassP trying 2nd order JacobiSN differential order: 2; trying a linearization to 3rd order trying 2nd order ODE linearizable_by_differentiation trying 2nd order, 2 integrating factors of the form mu(x,y) trying differential order: 2; missing variables -> trying 2nd order, dynamical_symmetries, fully reducible to Abel through one integrating factor of the form G(x,y)/(1+H(x,y)*y)^2 trying 2nd order, integrating factors of the form mu(x,y)/(y)^n, only the singular cases trying symmetries linear in x and y(x) trying differential order: 2; exact nonlinear trying 2nd order, integrating factor of the form mu(y) trying 2nd order, integrating factor of the form mu(x,y) trying 2nd order, integrating factor of the form mu(x,y)/(y)^n, only the general case trying 2nd order, integrating factor of the form mu(y,y) trying differential order: 2; mu polynomial in y trying 2nd order, integrating factor of the form mu(x,y) differential order: 2; looking for linear symmetries -> trying 2nd order, the S-function method -> trying a change of variables {x -> y(x), y(x) -> x} and re-entering methods for the S-function -> trying 2nd order, the S-function method -> trying 2nd order, No Point Symmetries Class V -> trying 2nd order, No Point Symmetries Class V -> trying 2nd order, No Point Symmetries Class V trying 2nd order, integrating factor of the form mu(x,y)/(y)^n, only the general case -> trying 2nd order, dynamical_symmetries, only a reduction of order through one integrating factor of the form G(x,y)/(1+H(x,y)*y)^ --- Trying Lie symmetry methods, 2nd order --- `, `-> Computing symmetries using: way = 3 `, `-> Computing symmetries using: way = 5 `, `-> Computing symmetries using: way = formal`
✗ Solution by Maple
dsolve(3*y(x)*diff(y(x),x$2)=sin(x),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[3*y[x]*y''[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
Not solved