Internal problem ID [1504]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined
Coefficients for Higher Order Equations. Page 495
Problem number: section 9.3, problem 7.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y+{\mathrm e}^{-2 x} \left (1-15 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve(4*diff(y(x),x$3)+8*diff(y(x),x$2)-diff(y(x),x)-2*y(x)=-exp(-2*x)*(1-15*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (2+x \right ) {\mathrm e}^{-2 x}}{2}+{\mathrm e}^{-2 x} c_{1}+c_{2} {\mathrm e}^{-\frac {x}{2}}+c_{3} {\mathrm e}^{\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 44
DSolve[4*y'''[x]+8*y''[x]-y'[x]-2*y[x]==-Exp[-2*x]*(1-15*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{10} e^{-2 x} \left (5 x (x+2)+10 e^{3 x/2} \left (c_2 e^x+c_1\right )+8+10 c_3\right ) \\ \end{align*}