83.2.9 problem 9

Internal problem ID [19055]
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 (A) at page 8
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 12:49:31 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(x*diff(y(x),x)-y(x)-cos(1/x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 16

DSolve[x*D[y[x],x]-y[x]-Cos[1/x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (-\sin \left (\frac {1}{x}\right )+c_1\right ) \]