Internal problem ID [3337]
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]
\[ \boxed {y^{\prime }-y \sec \left (x \right )=\left (\sin \left (x \right )-1\right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x) = y(x)*sec(x)+(sin(x)-1)^2,y(x), singsol=all)
\[ y \left (x \right ) = \left (-3 \sin \left (x \right )+4 \ln \left (\sec \left (x \right )+\tan \left (x \right )\right )+4 \ln \left (\cos \left (x \right )\right )-\frac {\cos \left (2 x \right )}{4}+c_{1} \right ) \left (\sec \left (x \right )+\tan \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 12.2 (sec). Leaf size: 50
DSolve[y'[x]==y[x] Sec[x]+(Sin[x]-1)^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{4} e^{2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )} \left (\cos (2 x)-4 \left (-3 \sin (x)+8 \log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )+c_1\right )\right ) \]