35.6.28 problem 34

Internal problem ID [6178]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 34
Date solved : Monday, January 27, 2025 at 01:46:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{x}+6 x -5 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=2*exp(x)+6*x-5,y(x), singsol=all)
 

\[ y = c_2 \,{\mathrm e}^{3 x}+c_1 \,{\mathrm e}^{2 x}+{\mathrm e}^{x}+x \]

✓ Solution by Mathematica

Time used: 0.260 (sec). Leaf size: 26

DSolve[D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==2*Exp[x]+6*x-5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x+e^x+c_1 e^{2 x}+c_2 e^{3 x} \]