Internal problem ID [1561]
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 64.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y-\left (x +1\right ) {\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 40
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=exp(x)*(1+x),y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {1}{24} x^{3}+\frac {1}{8} x^{2}\right ) \left ({\mathrm e}^{x}+x \,{\mathrm e}^{x}\right )+c_{1} {\mathrm e}^{x}+c_{2} x \,{\mathrm e}^{x}+c_{3} {\mathrm e}^{x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 36
DSolve[y'''[x]-3*y''[x]+3*y'[x]-1*y[x]==Exp[x]*(1+x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{24} e^x (x (x (x (x+4)+24 c_3)+24 c_2)+24 c_1) \\ \end{align*}