Internal problem ID [2628]
Book: An introduction to the solution and applications of differential equations, J.W. Searl,
1966
Section: Chapter 4, Ex. 4.1
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {\cos \relax (y)-x \sin \relax (y) y^{\prime }-\left (\sec ^{2}\relax (x )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.953 (sec). Leaf size: 17
dsolve([cos(y(x))-x*sin(y(x))*diff(y(x),x)=sec(x)^2,y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {\tan \relax (x )}{x}\right ) \left (1-2 \_B13 \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{Cos[y[x]]-x*Sin[y[x]]*y'[x]==Sec[x]^2,y[0]==0},y[x],x,IncludeSingularSolutions -> True]
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