Internal problem ID [2527]
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 \left (x \right )=0} \end {gather*}
✓ 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*}