Internal problem ID [13476]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.1 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }=8 \,{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)+2*diff(y(x),x)=8*exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-2 x} c_{1}}{2}+{\mathrm e}^{2 x}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 24
DSolve[y''[x]+2*y'[x]==8*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x}-\frac {1}{2} c_1 e^{-2 x}+c_2 \]