55.1.12 problem HW 5 problem 2

Internal problem ID [8708]
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
Date solved : Monday, January 27, 2025 at 04:19:56 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)+y(x)=tan(x)^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.080 (sec). Leaf size: 23

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

\[ y(x)\to \sin (x) \text {arctanh}(\sin (x))+c_1 \cos (x)+c_2 \sin (x)-2 \]