Internal problem ID [5175]
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]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=x^{2}-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=x^2-1,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} c_{2} +{\mathrm e}^{x} x c_{1} +x^{2}+4 x +5 \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 26
DSolve[y''[x]-2*y'[x]+y[x]==x^2-1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2+x \left (4+c_2 e^x\right )+c_1 e^x+5 \]