83.5.3 problem 3

Internal problem ID [19098]
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 (D) at page 16
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 12:56:00 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 17

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

\[ y(x)\to \frac {\sin (x)+c_1 \cos (x)}{x} \]