Internal problem ID [4675]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. Supplementary
Problems. page 101
Problem number: Problem 11.52.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y-1-{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 29
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=exp(x)+1,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{x} x^{3}}{6}-1+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{x} x +c_{3} {\mathrm e}^{x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 31
DSolve[y'''[x]-3*y''[x]+3*y'[x]-y[x]==Exp[x]+1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1+e^x \left (\frac {x^3}{6}+c_3 x^2+c_2 x+c_1\right ) \\ \end{align*}