38.2.42 problem 42

Internal problem ID [6471]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 42
Date solved : Monday, January 27, 2025 at 02:07:02 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 17

dsolve([diff(y(x),x)+y(x)/x=sin(x),y(1/2*Pi) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 18

DSolve[{D[y[x],x]+y[x]/x==Sin[x],{y[Pi/2]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sin (x)-x \cos (x)-1}{x} \]