27.1.4 problem 4

Internal problem ID [4298]
Book : An introduction to the solution and applications of differential equations, J.W. Searl, 1966
Section : Chapter 4, Ex. 4.1
Problem number : 4
Date solved : Monday, January 27, 2025 at 08:50:12 AM
CAS classification : [_exact]

\begin{align*} \cos \left (y\right )-x \sin \left (y\right ) y^{\prime }&=\sec \left (x \right )^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 1.208 (sec). Leaf size: 23

dsolve([cos(y(x))-x*sin(y(x))*diff(y(x),x)=sec(x)^2,y(0) = 0],y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \arccos \left (\frac {\tan \left (x \right )}{x}\right ) \\ y \left (x \right ) &= -\arccos \left (\frac {\tan \left (x \right )}{x}\right ) \\ \end{align*}

✗ Solution by Mathematica

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

DSolve[{Cos[y[x]]-x*Sin[y[x]]*D[y[x],x]==Sec[x]^2,y[0]==0},y[x],x,IncludeSingularSolutions -> True]
 

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