2.61 problem Problem 20(h)

Internal problem ID [10934]

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).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

\[ \boxed {y^{\prime \prime }+\left (2 x +5\right ) y^{\prime }+\left (4 x +8\right ) y-{\mathrm e}^{-2 x}=0} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 37

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)
 

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

Solution by Mathematica

Time used: 0.103 (sec). Leaf size: 45

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

\begin{align*} y(x)\to \frac {1}{2} e^{-x (x+3)} \left (e^{x^2+x} \left (1+(-1+2 c_2) \operatorname {DawsonF}\left (x+\frac {1}{2}\right )\right )+2 c_1\right ) \\ \end{align*}