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*}