7.11.33 problem 34

Internal problem ID [354]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 34
Date solved : Wednesday, February 05, 2025 at 03:29:50 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 14

dsolve([diff(y(x),x$2)+y(x)=cos(x),y(0) = 1, D(y)(0) = -1],y(x), singsol=all)
 

\[ y = \frac {\left (x -2\right ) \sin \left (x \right )}{2}+\cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 17

DSolve[{D[y[x],{x,2}]+y[x]==Cos[x],{y[0]==1,Derivative[1][y][0] ==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} (x-2) \sin (x)+\cos (x) \]