83.5.4 problem 4

Internal problem ID [19099]
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 : 4
Date solved : Tuesday, January 28, 2025 at 12:56:06 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve((y(x)-x*sin(x^2))+x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-\frac {\cos \left (x^{2}\right )}{2}+c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 21

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

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