Internal problem ID [2527]
Internal file name [OUTPUT/2019_Sunday_June_05_2022_02_44_52_AM_32039854/index.tex]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page
523
Problem number: Problem 15.33.
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, _exact, _nonlinear]]
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 trying differential order: 3; exact nonlinear -> Calling odsolve with the ODE`, (diff(_b(_a), _a))^2+(diff(_b(_a), _a))*_b(_a)+(diff(diff(_b(_a), _a), _a))*_b(_a)+(1/2)*cos(_a)+c 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 a quadrature checking if the LODE has constant coefficients <- constant coefficients successful <- 2nd order, 2 integrating factors of the form mu(x,y) successful <- differential order: 3; exact nonlinear successful`
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 81
dsolve(2*y(x)*diff(y(x),x$3)+2*(y(x)+3*diff(y(x),x))*diff(y(x),x$2)+2*(diff(y(x),x))^2=sin(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\sqrt {2}\, \sqrt {-4 \left (\left (-\frac {\cos \left (x \right )}{4}+\frac {\sin \left (x \right )}{4}+c_{1} \left (x -1\right )+c_{3} \right ) {\mathrm e}^{x}-c_{2} \right ) {\mathrm e}^{x}}\, {\mathrm e}^{-x}}{2} \\ y \left (x \right ) &= \frac {\sqrt {2}\, \sqrt {-4 \left (\left (-\frac {\cos \left (x \right )}{4}+\frac {\sin \left (x \right )}{4}+c_{1} \left (x -1\right )+c_{3} \right ) {\mathrm e}^{x}-c_{2} \right ) {\mathrm e}^{x}}\, {\mathrm e}^{-x}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.473 (sec). Leaf size: 88
DSolve[2*y[x]*y'''[x]+2*(y[x]+3*y'[x])*y''[x]+2*(y'[x])^2==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-\sin (x)+\cos (x)+2 c_1 x+2 c_3 e^{-x}-2 c_1-4 c_2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-\sin (x)+\cos (x)+2 c_1 x+2 c_3 e^{-x}-2 c_1-4 c_2}}{\sqrt {2}} \\ \end{align*}