29.3.19 problem 73

Internal problem ID [4681]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 3
Problem number : 73
Date solved : Monday, January 27, 2025 at 09:31:26 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=y \sec \left (x \right )+\left (\sin \left (x \right )-1\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (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: 12.261 (sec). Leaf size: 55

DSolve[D[y[x],x]==y[x] Sec[x]+(Sin[x]-1)^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{4} e^{2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )} (\cos (2 x)+4 (4 i x+3 \sin (x)-8 \log (\cos (x)+i (\sin (x)+1))-c_1)) \]