Internal problem ID [3291]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-y \tan \left (x \right )=\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x) = cos(x)+y(x)*tan(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\frac {x}{2}+\frac {\sin \left (2 x \right )}{4}+c_{1}}{\cos \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 21
DSolve[y'[x]==Cos[x]+y[x]*Tan[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} (\sin (x)+(x+2 c_1) \sec (x)) \]