83.3.14 problem 14

Internal problem ID [19070]
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 : 14
Date solved : Tuesday, January 28, 2025 at 12:51:14 PM
CAS classification : [_separable]

\begin{align*} \left (\sin \left (y\right )+y \cos \left (y\right )\right ) y^{\prime }-\left (2 \ln \left (x \right )+1\right ) x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 18

dsolve((sin(y(x))+y(x)*cos(y(x)))*diff(y(x),x)-(2*ln(x)+1)*x=0,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: 0.518 (sec). Leaf size: 22

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

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