Internal problem ID [6000]
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]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-2 y=x^{2}+\cos \left (x \right )} \]
✓ 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: 0.142 (sec). Leaf size: 44
DSolve[y''[x]-y'[x]-2*y[x]==x^2+Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{20} \left (-10 x^2+10 x-2 \sin (x)-6 \cos (x)-15\right )+c_1 e^{-x}+c_2 e^{2 x} \]