Internal problem ID [2828]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 73.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-y \sec \relax (x )-\left (\sin \relax (x )-1\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 35
dsolve(diff(y(x),x) = y(x)*sec(x)+(sin(x)-1)^2,y(x), singsol=all)
\[ y \relax (x ) = \left (-\frac {\left (\cos ^{2}\relax (x )\right )}{2}-3 \sin \relax (x )+4 \ln \left (\cos \relax (x )\right )+4 \ln \left (\sec \relax (x )+\tan \relax (x )\right )+c_{1}\right ) \left (\sec \relax (x )+\tan \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.245 (sec). Leaf size: 50
DSolve[y'[x]==y[x] Sec[x]+(Sin[x]-1)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{4} e^{2 \tanh ^{-1}\left (\tan \left (\frac {x}{2}\right )\right )} \left (\cos (2 x)-4 \left (-3 \sin (x)+8 \log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )+c_1\right )\right ) \\ \end{align*}