8.3.3 problem 3

Internal problem ID [679]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 3
Date solved : Monday, January 27, 2025 at 02:57:35 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=y \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 11

dsolve(diff(y(x),x) = sin(x)*y(x),y(x), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{-\cos \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 19

DSolve[D[y[x],x] == Sin[x]*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{-\cos (x)} \\ y(x)\to 0 \\ \end{align*}