56.1.11 problem 11

Internal problem ID [8723]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 11
Date solved : Monday, January 27, 2025 at 04:20:32 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=x +\frac {\sec \left (x \right ) y}{x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 31

dsolve(diff(y(x),x) = x+sec(x)*y(x)/x,y(x), singsol=all)
 

\[ y = \left (\int x \,{\mathrm e}^{-\int \frac {\sec \left (x \right )}{x}d x}d x +c_{1} \right ) {\mathrm e}^{\int \frac {\sec \left (x \right )}{x}d x} \]

✓ Solution by Mathematica

Time used: 0.255 (sec). Leaf size: 56

DSolve[D[y[x],x] == x+Sec[x]*y[x]/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {\sec (K[1])}{K[1]}dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}\frac {\sec (K[1])}{K[1]}dK[1]\right ) K[2]dK[2]+c_1\right ) \]