Internal problem ID [909]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+2 \sin \relax (x ) \cos \relax (x ) y-{\mathrm e}^{-\left (\sin ^{2}\relax (x )\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x) +(2*sin(x)*cos(x))*y(x)=exp(-sin(x)^2),y(x), singsol=all)
\[ y \relax (x ) = \left (c_{1}+x \right ) {\mathrm e}^{-\frac {1}{2}+\frac {\cos \left (2 x \right )}{2}} \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 24
DSolve[y'[x] +(2*Sin[x]*Cos[x])*y[x]==Exp[-Sin[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (x+\sqrt {e} c_1\right ) e^{-\sin ^2(x)} \\ \end{align*}