Internal problem ID [6302]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-x -\frac {\sec \relax (x ) y}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 35
dsolve(diff(y(x),x) = x+sec(x)*y(x)/x,y(x), singsol=all)
\[ y \relax (x ) = \left (\int x \,{\mathrm e}^{-\left (\int \frac {1}{\cos \relax (x ) x}d x \right )}d x +c_{1}\right ) {\mathrm e}^{\int \frac {1}{\cos \relax (x ) x}d x} \]
✓ Solution by Mathematica
Time used: 0.43 (sec). Leaf size: 56
DSolve[y'[x] == x+Sec[x]*y[x]/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \exp \left (\int _1^x\frac {\sec (K[1])}{K[1]}dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}\frac {\sec (K[1])}{K[1]}dK[1]\right ) K[2]dK[2]+c_1\right ) \\ \end{align*}