Internal problem ID [2520]
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]]
\[ \boxed {y^{\prime \prime \prime }-12 y^{\prime }+16 y=32 x -8} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$3)-12*diff(y(x),x)+16*y(x)=32*x-8,y(x), singsol=all)
\[ y \left (x \right ) = \left (\left (2 x +1\right ) {\mathrm e}^{4 x}+\left (c_{3} x +c_{2} \right ) {\mathrm e}^{6 x}+c_{1} \right ) {\mathrm e}^{-4 x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 35
DSolve[y'''[x]-12*y'[x]+16*y[x]==32*x-8,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-4 x}+c_2 e^{2 x}+x \left (2+c_3 e^{2 x}\right )+1 \]