58.1.28 problem 28

Internal problem ID [9099]
Book : Second order enumerated odes
Section : section 1
Problem number : 28
Date solved : Monday, January 27, 2025 at 05:39:20 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 43

dsolve(diff(y(x),x$2)+diff(y(x),x)+y(x)=1+x+x^2+x^3,y(x), singsol=all)
 

\[ y = c_{2} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) c_{1} +x^{3}-2 x^{2}-x +6 \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 60

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

\[ y(x)\to x^3-2 x^2-x+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+6 \]