Internal problem ID [2199]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 22, page 99
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y={\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=exp(3*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{3 x} \left (c_{2} +c_{1} x +\frac {1}{2} x^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 27
DSolve[y''[x]-6*y'[x]+9*y[x]==Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{3 x} \left (x^2+2 c_2 x+2 c_1\right ) \]