Internal problem ID [13685]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 21. Nonhomogeneous equations in general. Additional exercises page
391
Problem number: 21.13 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y={\mathrm e}^{4 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=exp(4*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (-6 c_{2} {\mathrm e}^{7 x}+{\mathrm e}^{6 x}-6 c_{1} \right ) {\mathrm e}^{-2 x}}{6} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 31
DSolve[y''[x]-3*y'[x]-10*y[x]==Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {e^{4 x}}{6}+c_1 e^{-2 x}+c_2 e^{5 x} \]