7.11.53 problem 55

Internal problem ID [374]
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 : 55
Date solved : Wednesday, February 05, 2025 at 03:26:22 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=\sin \left (x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 30

dsolve(diff(y(x),x$2)+4*y(x)=sin(x)^2,y(x), singsol=all)
 

\[ y = \frac {\left (8 c_1 -1\right ) \cos \left (2 x \right )}{8}+\frac {1}{8}+\frac {\left (8 c_2 -x \right ) \sin \left (2 x \right )}{8} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 34

DSolve[D[y[x],{x,2}]+4*y[x]==Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} ((-1+8 c_1) \cos (2 x)-(x-8 c_2) \sin (2 x)+1) \]