83.8.25 problem 26

Internal problem ID [19151]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 01:09:20 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Solution by Maple

dsolve(diff(y(x),x)+tan(y(x))/x=1/x^2*tan(y(x))*sin(y(x)),y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.629 (sec). Leaf size: 23

DSolve[D[y[x],x]+Tan[y[x]]/x==1/x^2*Tan[y[x]]*Sin[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \csc ^{-1}\left (\frac {1}{2 x}+c_1 x\right ) \\ y(x)\to 0 \\ \end{align*}