Internal problem ID [13780]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 24. Variation of parameters. Additional exercises page 444
Problem number: 24.1 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-7 y^{\prime }+10 y=6 \,{\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-7*diff(y(x),x)+10*y(x)=6*exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{5 x} c_{2} +{\mathrm e}^{2 x} c_{1} -3 \,{\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 27
DSolve[y''[x]-7*y'[x]+10*y[x]==6*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} \left (-3 e^x+c_2 e^{3 x}+c_1\right ) \]