29.1.13 problem 12

Internal problem ID [4620]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 12
Date solved : Monday, January 27, 2025 at 09:26:29 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.128 (sec). Leaf size: 14

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

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