Internal problem ID [3394]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 137.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-y \sec \left (x \right ) \operatorname {Csx} \left (x \right )=\sec \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x) = sec(x)^2+y(x)*sec(x)*Csx(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\int \sec \left (x \right )^{2} {\mathrm e}^{-\left (\int \operatorname {Csx} \left (x \right ) \sec \left (x \right )d x \right )}d x +c_{1} \right ) {\mathrm e}^{\int \operatorname {Csx} \left (x \right ) \sec \left (x \right )d x} \]
✓ Solution by Mathematica
Time used: 0.135 (sec). Leaf size: 57
DSolve[y'[x]==Sec[x]^2+y[x] Sec[x]Csx[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \exp \left (\int _1^x\text {Csx}(K[1]) \sec (K[1])dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}\text {Csx}(K[1]) \sec (K[1])dK[1]\right ) \sec ^2(K[2])dK[2]+c_1\right ) \]