Internal problem ID [2011]
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 15.9(a).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-12 y^{\prime }+16 y-32 x +8=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 28
dsolve(diff(y(x),x$3)-12*diff(y(x),x)+16*y(x)=32*x-8,y(x), singsol=all)
\[ y \relax (x ) = 1+2 x +{\mathrm e}^{-4 x} c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{2 x} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 31
DSolve[y'''[x]-12*y'[x]+16*y[x]==32*x-8,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 x+c_1 e^{-4 x}+e^{2 x} (c_3 x+c_2)+1 \\ \end{align*}