Internal problem ID [6863]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=12 x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=12*x^2,y(x), singsol=all)
\[ y \left (x \right ) = -{\mathrm e}^{-2 x} c_{1} +c_{2} {\mathrm e}^{-x}+6 x^{2}-18 x +21 \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 31
DSolve[y''[x]+3*y'[x]+2*y[x]==12*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 6 x^2-18 x+c_1 e^{-2 x}+c_2 e^{-x}+21 \]