58.1.27 problem 27

Internal problem ID [9098]
Book : Second order enumerated odes
Section : section 1
Problem number : 27
Date solved : Monday, January 27, 2025 at 05:38:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 37

dsolve(diff(y(x),x$2)+diff(y(x),x)+y(x)=1+x+x^2,y(x), singsol=all)
 

\[ y = c_{2} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) c_{1} +x^{2}-x \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 54

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

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