Internal problem ID [13366]
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 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }-10 y={\mathrm e}^{5 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-3*diff(y(x),x)-10*y(x)=exp(5*x),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{-2 x}+c_{1} {\mathrm e}^{5 x}+\frac {x \,{\mathrm e}^{5 x}}{7} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 31
DSolve[y''[x]-3*y'[x]-10*y[x]==Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-2 x}+e^{5 x} \left (\frac {x}{7}-\frac {1}{49}+c_2\right ) \]