62.36.9 problem Ex 10

Internal problem ID [13007]
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
Date solved : Tuesday, January 28, 2025 at 04:49:05 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }+2 \tan \left (x \right ) {y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 21

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)
 

\[ y = -\frac {{\mathrm e}^{\frac {c_{1}}{2}} \operatorname {Ei}_{1}\left (\ln \left (\tan \left (x \right )\right )+\frac {c_{1}}{2}\right )}{2}+c_{2} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],{x,2}]+2*Cot[x]*D[y[x],x]+2*Tan[x]*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved