Internal problem ID [11262]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 49. Variation
of parameters. Page 106
Problem number: Ex 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\tan \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+y(x)=tan(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +c_{1} \cos \left (x \right )-\cos \left (x \right ) \ln \left (\sec \left (x \right )+\tan \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 23
DSolve[y''[x]+y[x]==Tan[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cos (x) (-\text {arctanh}(\sin (x)))+c_1 \cos (x)+c_2 \sin (x) \]