83.3.10 problem 10

Internal problem ID [19066]
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 : 10
Date solved : Tuesday, January 28, 2025 at 12:50:07 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.573 (sec). Leaf size: 49

dsolve(csc(x)*ln(y(x))*diff(y(x),x)+x^2*y(x)^2=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\operatorname {LambertW}\left (\left (x^{2} \cos \left (x \right )-2 \sin \left (x \right ) x -2 \cos \left (x \right )-c_{1} \right ) {\mathrm e}^{-1}\right )}{x^{2} \cos \left (x \right )-2 \sin \left (x \right ) x -2 \cos \left (x \right )-c_{1}} \]

✓ Solution by Mathematica

Time used: 60.095 (sec). Leaf size: 45

DSolve[Csc[x]*Log[y[x]]*D[y[x],x]+x^2*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {W\left (\frac {\left (x^2-2\right ) \cos (x)-2 x \sin (x)+c_1}{e}\right )}{\left (x^2-2\right ) \cos (x)-2 x \sin (x)+c_1} \]