Internal problem ID [2196]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 20, page 90
Problem number: 23.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime }=\tan \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 83
dsolve(diff(y(x),x$3)+diff(y(x),x)=tan(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {i \left ({\mathrm e}^{i x}-{\mathrm e}^{-i x}\right ) \ln \left (\frac {i {\mathrm e}^{i x}-1}{-{\mathrm e}^{i x}+i}\right )}{2}+c_{1} \sin \left (x \right )-c_{2} \cos \left (x \right )-\ln \left ({\mathrm e}^{i x}-i\right )-\ln \left ({\mathrm e}^{i x}+i\right )+c_{3} +\ln \left ({\mathrm e}^{i x}\right ) \]
✓ Solution by Mathematica
Time used: 0.101 (sec). Leaf size: 35
DSolve[y'''[x]+y'[x]==Tan[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\sin (x) \text {arctanh}(\sin (x))-\frac {1}{2} \log \left (\cos ^2(x)\right )-c_2 \cos (x)+c_1 \sin (x)+c_3 \]