Internal problem ID [2018]
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.
CAS Maple gives this as type [[_3rd_order, _exact, _nonlinear]]
Solve \begin {gather*} \boxed {2 y y^{\prime \prime \prime }+2 \left (y+3 y^{\prime }\right ) y^{\prime \prime }+2 \left (y^{\prime }\right )^{2}-\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 93
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 \relax (x ) = -\frac {{\mathrm e}^{-x} \sqrt {-2 \,{\mathrm e}^{x} \left (4 x \,{\mathrm e}^{x} c_{1}+\sin \relax (x ) {\mathrm e}^{x}-\cos \relax (x ) {\mathrm e}^{x}-4 \,{\mathrm e}^{x} c_{1}+4 c_{3} {\mathrm e}^{x}-4 c_{2}\right )}}{2} \\ y \relax (x ) = \frac {{\mathrm e}^{-x} \sqrt {-2 \,{\mathrm e}^{x} \left (4 x \,{\mathrm e}^{x} c_{1}+\sin \relax (x ) {\mathrm e}^{x}-\cos \relax (x ) {\mathrm e}^{x}-4 \,{\mathrm e}^{x} c_{1}+4 c_{3} {\mathrm e}^{x}-4 c_{2}\right )}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.255 (sec). Leaf size: 84
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-1)+2 c_3 e^{-x}-4 c_2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-\sin (x)+\cos (x)+2 c_1 (x-1)+2 c_3 e^{-x}-4 c_2}}{\sqrt {2}} \\ \end{align*}