Internal problem ID [10317]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 60.
Exact equation. Integrating factor. Page 139
Problem number: Ex 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 \cot \relax (x ) y^{\prime }+2 \tan \relax (x ) \left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(diff(y(x),x$2)+2*cot(x)*diff(y(x),x)+2*tan(x)*diff(y(x),x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {{\mathrm e}^{\frac {c_{1}}{2}} \expIntegral \left (1, \ln \left (\frac {i \left (-{\mathrm e}^{2 i x}+1\right )}{{\mathrm e}^{2 i x}+1}\right )+\frac {c_{1}}{2}\right )}{2}+c_{2} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x]+2*Cot[x]*y'[x]+2*Tan[x]*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
Not solved