83.13.2 problem 3

Internal problem ID [19178]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (E) at page 39
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:11:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.138 (sec). Leaf size: 55

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

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