83.3.8 problem 8

Internal problem ID [19064]
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 : 8
Date solved : Tuesday, January 28, 2025 at 12:50:01 PM
CAS classification : [_separable]

\begin{align*} \frac {\cos \left (y\right )^{2} y^{\prime }}{x}+\frac {\cos \left (x \right )^{2}}{y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.132 (sec). Leaf size: 40

dsolve(1/x*cos(y(x))^2*diff(y(x),x)+( 1/y(x)*cos(x)^2 )=0,y(x), singsol=all)
 

\[ c_{1} +x^{2}+y \left (x \right )^{2}-1+\sin \left (2 x \right ) x +\frac {\cos \left (2 x \right )}{2}+y \left (x \right ) \sin \left (2 y \left (x \right )\right )+\frac {\cos \left (2 y \left (x \right )\right )}{2} = 0 \]

✓ Solution by Mathematica

Time used: 0.781 (sec). Leaf size: 65

DSolve[1/x*Cos[y[x]]^2*D[y[x],x]+( 1/y[x]*Cos[x]^2 )==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {InverseFunction}\left [2 \left (\frac {\text {$\#$1}^2}{4}+\frac {1}{4} \text {$\#$1} \sin (2 \text {$\#$1})+\frac {1}{8} \cos (2 \text {$\#$1})\right )\&\right ]\left [\frac {1}{4} \left (-\cos (2 x)-2 \left (x^2+x \sin (2 x)-2 c_1\right )\right )\right ] \]