Internal problem ID [13509]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 25. Review exercises for part III. page 447
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-9 y^{\prime }+14 y=98 x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-9*diff(y(x),x)+14*y(x)=98*x^2,y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{7 x}+c_{1} {\mathrm e}^{2 x}+7 x^{2}+9 x +\frac {67}{14} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 33
DSolve[y''[x]-9*y'[x]+14*y[x]==98*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 7 x^2+9 x+c_1 e^{2 x}+c_2 e^{7 x}+\frac {67}{14} \]