Internal problem ID [1050]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {-\sin \left (x \right ) y+y^{\prime } \cos \left (x \right )=-\sin \left (x \right )+2 \cos \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 10
dsolve([(sin(x)-y(x)*sin(x)-2*cos(x))+(cos(x))*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = 2 \tan \left (x \right )+1 \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 11
DSolve[{(Sin[x]-y[x]*Sin[x]-2*Cos[x])+(Cos[x])*y'[x]==0,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 \tan (x)+1 \]