83.8.21 problem 22

Internal problem ID [19147]
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. Misc examples on chapter II at page 25
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 01:06:09 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x \left (2 \ln \left (x \right )+1\right )}{\sin \left (y\right )+y \cos \left (y\right )} \end{align*}

✓ Solution by Maple

Time used: 0.050 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.490 (sec). Leaf size: 22

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

\[ y(x)\to \text {InverseFunction}[\text {$\#$1} \sin (\text {$\#$1})\&]\left [x^2 \log (x)+c_1\right ] \]