Internal problem ID [4667]
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 11.44.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+y-x^{2}+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=x^2-1,y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+{\mathrm e}^{x} c_{1} x +x^{2}+4 x +5 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[y''[x]-2*y'[x]+y[x]==x^2-1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2+4 x+e^x (c_2 x+c_1)+5 \\ \end{align*}