Internal problem ID [6864]
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]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=x^{2}+2 x +1} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \frac {3}{4}-\frac {x}{2}+\frac {x^{2}}{2}-{\mathrm e}^{-2 x} c_{1} +c_{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 36
DSolve[y''[x]+3*y'[x]+2*y[x]==1+2*x+x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (2 x^2-2 x+3\right )+c_1 e^{-2 x}+c_2 e^{-x} \]