10.1 problem 1

Internal problem ID [1155]

Book: Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page 262
Problem number: 1.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y-\tan \left (3 x \right )=0} \end {gather*}

Solution by Maple

Time used: 0.004 (sec). Leaf size: 37

dsolve(diff(y(x),x$2)+9*y(x)=tan(3*x),y(x), singsol=all)
 

\[ y \relax (x ) = \sin \left (3 x \right ) c_{2}+\cos \left (3 x \right ) c_{1}-\frac {\cos \left (3 x \right ) \ln \left (\frac {1+\sin \left (3 x \right )}{\cos \left (3 x \right )}\right )}{9} \]

Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 31

DSolve[y''[x]+9*y[x]==Tan[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_2 \sin (3 x)-\frac {1}{9} \cos (3 x) \left (\tanh ^{-1}(\sin (3 x))-9 c_1\right ) \\ \end{align*}