77.1.131 problem 158 (page 236)

Internal problem ID [18021]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 158 (page 236)
Date solved : Tuesday, January 28, 2025 at 11:20:09 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 38

dsolve(diff(y(x),x$2)+diff(y(x),x)+y(x)=exp(-x/2)*sin(x*sqrt(3)/2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.146 (sec). Leaf size: 60

DSolve[D[y[x],{x,2}]+D[y[x],x]+y[x]==Exp[-x/2]*Sin[x*Sqrt[3]/2],y[x],x,IncludeSingularSolutions -> True]
 

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