Internal problem ID [4615]
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: 37.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {y}{x}-\sin \left (2 x \right )=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = 2\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 25
dsolve([diff(y(x),x)+1/x*y(x)=sin(2*x),y(1/4*Pi) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {-2 x \cos \left (2 x \right )+2 \pi +\sin \left (2 x \right )-1}{4 x} \]
✓ Solution by Mathematica
Time used: 0.094 (sec). Leaf size: 28
DSolve[{y'[x]+1/x*y[x]==Sin[2*x],{y[Pi/4]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sin (2 x)-2 x \cos (2 x)+2 \pi -1}{4 x} \\ \end{align*}