Internal problem ID [5246]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 93
Problem number: 1(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-2 y-x^{2}-\cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=x^2+cos(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{2 x} c_{2} +{\mathrm e}^{-x} c_{1} -\frac {x^{2}}{2}-\frac {3 \cos \left (x \right )}{10}-\frac {\sin \left (x \right )}{10}+\frac {x}{2}-\frac {3}{4} \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 45
DSolve[y''[x]-y'[x]-2*y[x]==x^2+Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x}+c_2 e^{2 x}+\frac {1}{20} (-5 (2 (x-1) x+3)-2 \sin (x)-6 \cos (x)) \\ \end{align*}