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: 117
dsolve(diff(y(x),x$3)+diff(y(x),x)=tan(x),y(x), singsol=all)
\[ y = c_{1} \sin \left (x \right )-c_{2} \cos \left (x \right )-\ln \left ({\mathrm e}^{i x}-i\right )-\ln \left (i+{\mathrm e}^{i x}\right )+\frac {i {\mathrm e}^{i x} \ln \left (\frac {-i {\mathrm e}^{2 i x}+i+2 \,{\mathrm e}^{i x}}{{\mathrm e}^{2 i x}+1}\right )}{2}+\ln \left ({\mathrm e}^{i x}\right )-\frac {i \ln \left (\frac {-i {\mathrm e}^{2 i x}+i+2 \,{\mathrm e}^{i x}}{{\mathrm e}^{2 i x}+1}\right ) {\mathrm e}^{-i x}}{2}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.101 (sec). Leaf size: 35
DSolve[y'''[x]+y'[x]==Tan[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\sin (x) \text {arctanh}(\sin (x))-\frac {1}{2} \log \left (\cos ^2(x)\right )-c_2 \cos (x)+c_1 \sin (x)+c_3 \]