67.2.61 problem Problem 20(h)

Internal problem ID [14018]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 20(h)
Date solved : Tuesday, January 28, 2025 at 06:12:52 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+\left (2 x +5\right ) y^{\prime }+\left (4 x +8\right ) y&={\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 35

dsolve(diff(y(x),x$2)+(2*x+5)*diff(y(x),x)+(4*x+8)*y(x)=exp(-2*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x \left (x +3\right )} c_{2} +{\mathrm e}^{-x \left (x +3\right )} \operatorname {erf}\left (i \left (x +\frac {1}{2}\right )\right ) c_{1} +\frac {{\mathrm e}^{-2 x}}{2} \]

✓ Solution by Mathematica

Time used: 0.319 (sec). Leaf size: 64

DSolve[D[y[x],{x,2}]+(2*x+5)*D[y[x],x]+(4*x+8)*y[x]==Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x (x+3)} \left (\int _1^x-\int _1^{K[2]}e^{K[1]^2+K[1]}dK[1]dK[2]+(x+c_2) \int _1^xe^{K[1]^2+K[1]}dK[1]+c_1\right ) \]