Internal problem ID [15410]
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: 641.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime } \tan \left (x \right )+\cos \left (x \right )^{2} y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \cos \left (\sin \left (x \right )\right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 15
dsolve([diff(y(x),x$2)+tan(x)*diff(y(x),x)+cos(x)^2*y(x)=0,cos(sin(x))],singsol=all)
\[ y \left (x \right ) = c_{1} \sin \left (\sin \left (x \right )\right )+c_{2} \cos \left (\sin \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 18
DSolve[y''[x]+Tan[x]*y'[x]+Cos[x]^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 \sin (\sin (x))+c_1 \cos (\sin (x)) \]