29.1.12 problem 11

Internal problem ID [4619]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 11
Date solved : Monday, January 27, 2025 at 09:26:27 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

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

\[ y \left (x \right ) = -\sin \left (x \right )-1+{\mathrm e}^{\sin \left (x \right )} c_{1} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 18

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

\[ y(x)\to -\sin (x)+c_1 e^{\sin (x)}-1 \]