Internal problem ID [13402]
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: 22.9 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=10 \,{\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=10*exp(3*x),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{3 x}+x \,{\mathrm e}^{3 x} c_{1} +5 x^{2} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 23
DSolve[y''[x]-6*y'[x]+9*y[x]==10*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{3 x} \left (5 x^2+c_2 x+c_1\right ) \]