Internal problem ID [9751]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1417.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\frac {\left (\sin \left (x \right )^{2}-\cos \left (x \right )\right ) y^{\prime }}{\sin \left (x \right )}+y \sin \left (x \right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 35
dsolve(diff(diff(y(x),x),x) = -(sin(x)^2-cos(x))/sin(x)*diff(y(x),x)-y(x)*sin(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {\cos \left (x \right )}{2}} \sin \left (\frac {\sqrt {3}\, \cos \left (x \right )}{2}\right )+c_{2} {\mathrm e}^{\frac {\cos \left (x \right )}{2}} \cos \left (\frac {\sqrt {3}\, \cos \left (x \right )}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.221 (sec). Leaf size: 45
DSolve[y''[x] == -(Sin[x]^2*y[x]) - Csc[x]*(-Cos[x] + Sin[x]^2)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{\frac {\cos (x)}{2}} \left (c_1 \cos \left (\frac {1}{2} \sqrt {3} \cos (x)\right )+c_2 \sin \left (\frac {1}{2} \sqrt {3} \cos (x)\right )\right ) \]