83.3.1 problem 1

Internal problem ID [19057]
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. Exercise II (B) at page 9
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 12:49:37 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.151 (sec). Leaf size: 25

dsolve(x*cos(y(x))^2=y(x)*cos(x)^2*diff(y(x),x),y(x), singsol=all)
 

\[ \tan \left (x \right ) x +\ln \left (\cos \left (x \right )\right )-y \left (x \right ) \tan \left (y \left (x \right )\right )-\ln \left (\cos \left (y \left (x \right )\right )\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.591 (sec). Leaf size: 55

DSolve[x*Cos[y[x]]^2==y[x]*Cos[x]^2*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {1}{2} (\text {$\#$1} \tan (\text {$\#$1})+\log (\cos (\text {$\#$1})))\&\right ]\left [\frac {1}{2} (x \tan (x)+\log (\cos (x)))+c_1\right ] \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}