Internal problem ID [11962]
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]]
\[ \boxed {y^{\prime \prime }+\left (2 x +5\right ) y^{\prime }+\left (4 x +8\right ) y={\mathrm e}^{-2 x}} \]
✓ 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: 0.333 (sec). Leaf size: 61
DSolve[y''[x]+(2*x+5)*y'[x]+(4*x+8)*y[x]==Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-x (x+3)-\frac {1}{4}} \left (\sqrt {\pi } (-1+2 c_2) \text {erfi}\left (x+\frac {1}{2}\right )+2 \left (e^{\left (x+\frac {1}{2}\right )^2}+2 \sqrt [4]{e} c_1\right )\right ) \]