12.2.23 problem 23

Internal problem ID [1559]
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
Date solved : Monday, January 27, 2025 at 05:00:06 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+2 \sin \left (x \right ) \cos \left (x \right ) y&={\mathrm e}^{-\sin \left (x \right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(diff(y(x),x) +(2*sin(x)*cos(x))*y(x)=exp(-sin(x)^2),y(x), singsol=all)
 

\[ y = \left (x +c_1 \right ) {\mathrm e}^{-\frac {1}{2}+\frac {\cos \left (2 x \right )}{2}} \]

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 24

DSolve[D[y[x],x] +(2*Sin[x]*Cos[x])*y[x]==Exp[-Sin[x]^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (x+\sqrt {e} c_1\right ) e^{-\sin ^2(x)} \]