62.29.9 problem Ex 10

Internal problem ID [12960]
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 10
Date solved : Tuesday, January 28, 2025 at 04:45:23 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 42

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

\[ y = \left (-2 \cos \left (x \right )^{2}+1\right ) \ln \left (\sec \left (x \right )\right )+2 c_{1} \cos \left (x \right )^{2}+2 \sin \left (x \right ) \left (x +c_{2} \right ) \cos \left (x \right )-\sin \left (x \right )^{2}-c_{1} \]

✓ Solution by Mathematica

Time used: 0.107 (sec). Leaf size: 49

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

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