Internal problem ID [2701]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 66.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\left (\sin \left (x \right )^{2}-y\right ) \cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x)=( sin(x)^2-y(x))*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {5}{2}+{\mathrm e}^{-\sin \left (x \right )} c_{1} -\frac {\cos \left (2 x \right )}{2}-2 \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.136 (sec). Leaf size: 30
DSolve[y'[x]==( Sin[x]^2-y[x])*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 \sin (x)-\frac {1}{2} \cos (2 x)+c_1 e^{-\sin (x)}+\frac {5}{2} \\ \end{align*}