73.17.31 problem 31

Internal problem ID [15565]
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
Date solved : Tuesday, January 28, 2025 at 08:02:12 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&=98 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (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)
 

\[ y = {\mathrm e}^{7 x} c_{2} +{\mathrm e}^{2 x} c_{1} +7 x^{2}+9 x +\frac {67}{14} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 33

DSolve[D[y[x],{x,2}]-9*D[y[x],x]+14*y[x]==98*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 7 x^2+9 x+c_1 e^{2 x}+c_2 e^{7 x}+\frac {67}{14} \]