58.1.25 problem 25

Internal problem ID [9096]
Book : Second order enumerated odes
Section : section 1
Problem number : 25
Date solved : Monday, January 27, 2025 at 05:37:45 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 50

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

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