Internal problem ID [13550]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 14. Higher order equations and the reduction of order method. Additional
exercises page 277
Problem number: 14.3 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+3 y=9 \,{\mathrm e}^{2 x}} \] Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{3 x} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)-4*diff(y(x),x)+3*y(x)=9*exp(2*x),exp(3*x)],singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{3 x}+c_{1} {\mathrm e}^{x}-9 \,{\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 25
DSolve[y''[x]-4*y'[x]+3*y[x]==9*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (-9 e^x+c_2 e^{2 x}+c_1\right ) \]