Internal problem ID [2201]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=x^2,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{3 x}+c_{1} {\mathrm e}^{2 x}+\frac {x^{2}}{6}+\frac {5 x}{18}+\frac {19}{108} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 37
DSolve[y''[x]-5*y'[x]+6*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2}{6}+\frac {5 x}{18}+c_1 e^{2 x}+c_2 e^{3 x}+\frac {19}{108} \]