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]]
\[ \boxed {y^{\prime \prime }+9 y=\tan \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)+9*y(x)=tan(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (3 x \right ) c_{2} +\cos \left (3 x \right ) c_{1} -\frac {\cos \left (3 x \right ) \ln \left (\sec \left (3 x \right )+\tan \left (3 x \right )\right )}{9} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 33
DSolve[y''[x]+9*y[x]==Tan[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{9} \cos (3 x) \text {arctanh}(\sin (3 x))+c_1 \cos (3 x)+c_2 \sin (3 x) \]