2.42 problem 42

Internal problem ID [4620]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }+\frac {y}{x}-\sin \relax (x )=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 0\right ] \end {align*}

Solution by Maple

Time used: 0.011 (sec). Leaf size: 17

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

\[ y \relax (x ) = \frac {-x \cos \relax (x )+\sin \relax (x )-1}{x} \]

Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 18

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

\begin{align*} y(x)\to \frac {\sin (x)-x \cos (x)-1}{x} \\ \end{align*}