Internal problem ID [6111]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 8. Nonhomogeneous Equations: Undetermined Coefficients. Exercises Page
142
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+2 y-x^{2}-2 x -1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=1+2*x+x^2,y(x), singsol=all)
\[ y \relax (x ) = -c_{1} {\mathrm e}^{-2 x}+\frac {3}{4}-\frac {x}{2}+\frac {x^{2}}{2}+c_{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 32
DSolve[y''[x]+3*y'[x]+2*y[x]==1+2*x+x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (x-1) x+e^{-2 x} \left (c_2 e^x+c_1\right )+\frac {3}{4} \\ \end{align*}