Internal problem ID [5128]
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]
\[ \boxed {y^{\prime }+\frac {y}{x}=\sin \left (x \right )} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve([diff(y(x),x)+y(x)/x=sin(x),y(1/2*Pi) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sin \left (x \right )-\cos \left (x \right ) x -1}{x} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 18
DSolve[{y'[x]+y[x]/x==Sin[x],{y[Pi/2]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sin (x)-x \cos (x)-1}{x} \]