Internal problem ID [15428]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.5 Linear equations with variable coefficients.
The Lagrange method. Exercises page 148
Problem number: 663.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime } \tan \left (x \right )=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)-2*tan(x)*diff(y(x),x)=1,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\ln \left (1+\cos \left (2 x \right )\right )}{4}+\frac {\ln \left (\cos \left (x \right )\right )}{2}+\frac {\left (4 c_{1} +2 x \right ) \tan \left (x \right )}{4}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 19
DSolve[y''[x]-2*Tan[x]*y'[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (\frac {x}{2}+c_1\right ) \tan (x)+c_2 \]