35.6.13 problem 13

Internal problem ID [6163]
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 : 13
Date solved : Monday, January 27, 2025 at 01:41:17 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=2 \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=2*cos(x),y(x), singsol=all)
 

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{x}-\sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 21

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

\[ y(x)\to -\sin (x)+e^x (c_2 x+c_1) \]