62.29.8 problem Ex 9

Internal problem ID [12959]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary. Page 117
Problem number : Ex 9
Date solved : Tuesday, January 28, 2025 at 04:45:19 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: 0.026 (sec). Leaf size: 34

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

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