Internal problem ID [2886]
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]
Solve \begin {gather*} \boxed {y^{\prime }-\left (\sec ^{2}\relax (x )\right )-y \sec \relax (x ) \mathit {Csx} \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 41
dsolve(diff(y(x),x) = sec(x)^2+y(x)*sec(x)*Csx(x),y(x), singsol=all)
\[ y \relax (x ) = \left (\int \frac {2 \,{\mathrm e}^{-\left (\int \frac {\mathit {Csx} \relax (x )}{\cos \relax (x )}d x \right )}}{\cos \left (2 x \right )+1}d x +c_{1}\right ) {\mathrm e}^{\int \frac {\mathit {Csx} \relax (x )}{\cos \relax (x )}d x} \]
✓ Solution by Mathematica
Time used: 0.132 (sec). Leaf size: 57
DSolve[y'[x]==Sec[x]^2+y[x] Sec[x]Csx[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ) \\ \end{align*}