Internal problem ID [13378]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.1 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }-5 y=30 \,{\mathrm e}^{-4 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)+4*diff(y(x),x)-5*y(x)=30*exp(-4*x),y(x), singsol=all)
\[ y = {\mathrm e}^{-5 x} c_{2} +c_{1} {\mathrm e}^{x}-6 \,{\mathrm e}^{-4 x} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 27
DSolve[y''[x]+4*y'[x]-5*y[x]==30*Exp[-4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-5 x} \left (-6 e^x+c_2 e^{6 x}+c_1\right ) \]