54.1.4 problem 4

Internal problem ID [8532]
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
Date solved : Monday, January 27, 2025 at 04:09:45 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=x^{2}+2 x +1 \end{align*}

✓ Solution by Maple

Time used: 0.002 (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)
 

\[ y = \frac {3}{4}+\frac {x^{2}}{2}-\frac {x}{2}-c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 36

DSolve[D[y[x],{x,2}]+3*D[y[x],x]+2*y[x]==1+2*x+x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (2 x^2-2 x+3\right )+c_1 e^{-2 x}+c_2 e^{-x} \]