Internal problem ID [1500]
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 3.
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}^{x} \left (6 x^{2}+45 x +4\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 64
dsolve(4*diff(y(x),x$3)+8*diff(y(x),x$2)-diff(y(x),x)-2*y(x)=-exp(x)*(4+45*x+6*x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (18 x^{2}+27 x -149\right ) \left (-6 x^{2} {\mathrm e}^{x}-45 x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{x}\right )}{162 x^{2}+1215 x +108}+{\mathrm e}^{-2 x} c_{1}+c_{2} {\mathrm e}^{-\frac {x}{2}}+c_{3} {\mathrm e}^{\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 51
DSolve[4*y'''[x]+8*y''[x]-y'[x]-2*y[x]==-Exp[x]*(4+45*x+6*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{27} e^x (149-9 x (2 x+3))+c_1 e^{-x/2}+c_2 e^{x/2}+c_3 e^{-2 x} \\ \end{align*}