Internal problem ID [13469]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 24. Variation of parameters. Additional exercises page 444
Problem number: 24.1 (m).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y=8 \,{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(x*diff(y(x),x$2)+(2+2*x)*diff(y(x),x)+2*y(x)=8*exp(2*x),y(x), singsol=all)
\[ y = \frac {{\mathrm e}^{-2 x} c_{2}}{x}+\frac {c_{1}}{x}+\frac {{\mathrm e}^{-2 x} {\mathrm e}^{4 x}}{x} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 31
DSolve[x*y''[x]+(2+2*x)*y'[x]+2*y[x]==8*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 e^{2 x}+2 c_1 e^{-2 x}+c_2}{2 x} \]