8.11.32 problem 55

Internal problem ID [900]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 55
Date solved : Wednesday, February 05, 2025 at 04:43:55 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: 0.003 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 71

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

\[ y(x)\to \cos (2 x) \int _1^x-\cos (K[1]) \sin (K[1])^2 \sin (K[1])dK[1]+\sin (2 x) \int _1^x\frac {1}{2} \cos (2 K[2]) \sin (K[2])^2dK[2]+c_1 \cos (2 x)+c_2 \sin (2 x) \]