83.45.9 problem Ex 9 page 56

Internal problem ID [19552]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter IV. Equations of the first order but not of the first degree
Problem number : Ex 9 page 56
Date solved : Tuesday, January 28, 2025 at 01:51:50 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\tan \left (x -\frac {y^{\prime }}{{y^{\prime }}^{2}+1}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 20

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

\[ y \left (x \right ) = \int \tan \left (\operatorname {RootOf}\left (\sin \left (\textit {\_Z} \right ) \cos \left (\textit {\_Z} \right )+\textit {\_Z} -x \right )\right )d x +c_{1} \]

✗ Solution by Mathematica

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

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

Timed out