Internal problem ID [2146]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential
Equations. page 59
Problem number: Problem 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\sin \relax (x ) y^{\prime }-\cos \relax (x ) y-\sin \left (2 x \right )=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 2\right ] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 14
dsolve([sin(x)*diff(y(x),x)-y(x)*cos(x)=sin(2*x),y(1/2*Pi) = 2],y(x), singsol=all)
\[ y \relax (x ) = \left (2 \ln \left (\sin \relax (x )\right )+2\right ) \sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 14
DSolve[{Sin[x]*y'[x]-y[x]*Cos[x]==Sin[2*x],{y[Pi/2]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \sin (x) (\log (\sin (x))+1) \\ \end{align*}