Internal problem ID [5416]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 18. Linear equations with variable coefficients (Equations of second order).
Supplemetary problems. Page 120
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)-2*tan(x)*diff(y(x),x)-10*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \sec \left (x \right ) \left (c_{1} \sinh \left (3 x \right )+c_{2} \cosh \left (3 x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 29
DSolve[y''[x]-2*Tan[x]*y'[x]-10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} e^{-3 x} \left (c_2 e^{6 x}+6 c_1\right ) \sec (x) \]