Internal problem ID [5184]
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]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime }=\sec \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 83
dsolve(diff(y(x),x$3)+diff(y(x),x)=sec(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {i \left ({\mathrm e}^{i x}-{\mathrm e}^{-i x}\right ) \ln \left (\frac {{\mathrm e}^{i x}}{{\mathrm e}^{2 i x}+1}\right )}{2}-\frac {i {\mathrm e}^{-i x}}{2}-2 i \arctan \left ({\mathrm e}^{i x}\right )+\frac {i {\mathrm e}^{i x}}{2}+\left (1+c_{1} -\ln \left (2\right )\right ) \sin \left (x \right )+\left (-x -c_{2} \right ) \cos \left (x \right )+c_{3} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 57
DSolve[y'''[x]+y'[x]==Sec[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -(x+c_2) \cos (x)-\log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )+\log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )+\sin (x) (\log (\cos (x))+c_1)+c_3 \]