18.2.8 problem Problem 15.9(a)

Internal problem ID [3491]
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)
Date solved : Monday, January 27, 2025 at 07:39:36 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-12 y^{\prime }+16 y&=32 x -8 \end{align*}

✓ Solution by Maple

Time used: 0.004 (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)
 

\[ y \left (x \right ) = {\mathrm e}^{-4 x} \left (\left (2 x +1\right ) {\mathrm e}^{4 x}+\left (x c_3 +c_{2} \right ) {\mathrm e}^{6 x}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 35

DSolve[D[y[x],{x,3}]-12*D[y[x],x]+16*y[x]==32*x-8,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-4 x}+c_2 e^{2 x}+x \left (2+c_3 e^{2 x}\right )+1 \]