Internal problem ID [13487]
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: 13.2 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }=9 \,{\mathrm e}^{-3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x$2)+4*diff(y(x),x)=9*exp(-3*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-4 x} c_{1}}{4}-3 \,{\mathrm e}^{-3 x}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 26
DSolve[y''[x]+4*y'[x]==9*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -3 e^{-3 x}-\frac {1}{4} c_1 e^{-4 x}+c_2 \]