Internal problem ID [4676]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 12. VARIATION OF PARAMETERS. page 104
Problem number: Problem 12.1.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+y^{\prime }-\sec \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 115
dsolve(diff(y(x),x$3)+diff(y(x),x)=sec(x),y(x), singsol=all)
\[ y \relax (x ) = \sin \relax (x ) c_{1}-x \cos \relax (x )+\sin \relax (x )-\cos \relax (x ) c_{2}+\frac {i \ln \relax (2) {\mathrm e}^{i x}}{2}-\frac {i \ln \relax (2) {\mathrm e}^{-i x}}{2}+\frac {i {\mathrm e}^{i x} \ln \left (\frac {{\mathrm e}^{i x}}{{\mathrm e}^{2 i x}+1}\right )}{2}-\frac {i {\mathrm e}^{-i x} \ln \left (\frac {{\mathrm e}^{i x}}{{\mathrm e}^{2 i x}+1}\right )}{2}+\frac {i {\mathrm e}^{i x}}{2}-\frac {i {\mathrm e}^{-i x}}{2}-2 i \arctan \left ({\mathrm e}^{i x}\right )+c_{3} \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 57
DSolve[y'''[x]+y'[x]==Sec[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -(x+c_2) \cos (x)-\log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )+\log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )+\sin (x) (\log (\cos (x))+c_1)+c_3 \\ \end{align*}