73.1.9 problem 2.2 (i)

Internal problem ID [14987]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.2 (i)
Date solved : Tuesday, January 28, 2025 at 07:26:40 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+8 y&={\mathrm e}^{-x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 121

dsolve(diff(y(x),x$2)+3*diff(y(x),x)+8*y(x)=exp(-x^2),y(x), singsol=all)
 

\[ y = -\frac {\sqrt {23}\, \operatorname {erf}\left (x -\frac {3}{4}+\frac {i \sqrt {23}}{4}\right ) \sqrt {\pi }\, \left (i \cos \left (\frac {\sqrt {23}\, x}{2}\right )-\sin \left (\frac {\sqrt {23}\, x}{2}\right )\right ) {\mathrm e}^{-\frac {3 x}{2}-\frac {7}{8}-\frac {3 i \sqrt {23}}{8}}}{46}+\frac {\sqrt {23}\, \left (i \cos \left (\frac {\sqrt {23}\, x}{2}\right )+\sin \left (\frac {\sqrt {23}\, x}{2}\right )\right ) \sqrt {\pi }\, \operatorname {erf}\left (x -\frac {3}{4}-\frac {i \sqrt {23}}{4}\right ) {\mathrm e}^{-\frac {3 x}{2}-\frac {7}{8}+\frac {3 i \sqrt {23}}{8}}}{46}+{\mathrm e}^{-\frac {3 x}{2}} \left (c_{1} \cos \left (\frac {\sqrt {23}\, x}{2}\right )+c_{2} \sin \left (\frac {\sqrt {23}\, x}{2}\right )\right ) \]

✓ Solution by Mathematica

Time used: 1.544 (sec). Leaf size: 146

DSolve[D[y[x],{x,2}]+3*D[y[x],x]+8*y[x]==Exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x/2} \left (\cos \left (\frac {\sqrt {23} x}{2}\right ) \int _1^x-\frac {2 e^{\frac {1}{2} (3-2 K[2]) K[2]} \sin \left (\frac {1}{2} \sqrt {23} K[2]\right )}{\sqrt {23}}dK[2]+\sin \left (\frac {\sqrt {23} x}{2}\right ) \int _1^x\frac {2 e^{\frac {1}{2} (3-2 K[1]) K[1]} \cos \left (\frac {1}{2} \sqrt {23} K[1]\right )}{\sqrt {23}}dK[1]+c_2 \cos \left (\frac {\sqrt {23} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {23} x}{2}\right )\right ) \]