2.9 problem Problem 11.52

Internal problem ID [5183]

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]]

\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y=1+{\mathrm e}^{x}} \]

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 27

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)
 

\[ y \left (x \right ) = -1+\frac {\left (6 c_{3} x^{2}+x^{3}+6 c_{2} x +6 c_{1} \right ) {\mathrm e}^{x}}{6} \]

✓ Solution by Mathematica

Time used: 0.067 (sec). Leaf size: 31

DSolve[y'''[x]-3*y''[x]+3*y'[x]-y[x]==Exp[x]+1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -1+e^x \left (\frac {x^3}{6}+c_3 x^2+c_2 x+c_1\right ) \]