Internal problem ID [3335]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 71.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\sin \left (x \right ) \left (2 \sec \left (x \right )^{2}-y\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x) = sin(x)*(2*sec(x)^2-y(x)),y(x), singsol=all)
\[ y \left (x \right ) = \left (2 \sec \left (x \right ) {\mathrm e}^{-\frac {1}{\sec \left (x \right )}}-2 \,\operatorname {Ei}_{1}\left (\frac {1}{\sec \left (x \right )}\right )+c_{1} \right ) {\mathrm e}^{\cos \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.13 (sec). Leaf size: 28
DSolve[y'[x]==Sin[x](2 Sec[x]^2-y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 e^{\cos (x)} \operatorname {ExpIntegralEi}(-\cos (x))+2 \sec (x)+c_1 e^{\cos (x)} \]