58.1.30 problem 30

Internal problem ID [9101]
Book : Second order enumerated odes
Section : section 1
Problem number : 30
Date solved : Monday, January 27, 2025 at 05:40:34 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y^{\prime }+y&=\cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 1.198 (sec). Leaf size: 50

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

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