Internal problem ID [6287]
Book: Selected problems from homeworks from different courses
Section: Math 2520, summer 2021. Differential Equations and Linear Algebra. Normandale college,
Bloomington, Minnesota
Problem number: HW 5 problem 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\left (\tan ^{2}\relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+y(x)=tan(x)^2,y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+\cos \relax (x ) c_{1}-2+\sin \relax (x ) \ln \left (\frac {\sin \relax (x )+1}{\cos \relax (x )}\right ) \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 50
DSolve[y''[x]+y[x]==Tan[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos (x)+\sin (x) \left (-\log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )+\log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )+c_2\right )-2 \\ \end{align*}