Internal problem ID [10270]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y-\left (\sec ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve(diff(y(x),x$2)+4*y(x)=sec(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 x \right ) c_{2}+\cos \left (2 x \right ) c_{1}+\frac {\left (2 \cos \relax (x ) x -\sin \relax (x )\right ) \sin \left (2 x \right )+2 \ln \left (\cos \relax (x )\right ) \cos \left (2 x \right ) \cos \relax (x )}{2 \cos \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 33
DSolve[y''[x]+4*y[x]==Sec[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cos (2 x) (\log (\cos (x))+c_1)+\sin (x) (-\sin (x)+2 (x+c_2) \cos (x)) \\ \end{align*}