15.12.23 problem 23

Internal problem ID [3167]
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
Date solved : Monday, January 27, 2025 at 07:24:48 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\tan \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 71

dsolve(diff(y(x),x$3)+diff(y(x),x)=tan(x),y(x), singsol=all)
 

\[ y = \frac {i \left ({\mathrm e}^{i x}-{\mathrm e}^{-i x}\right ) \ln \left (\frac {i {\mathrm e}^{i x}-1}{-{\mathrm e}^{i x}+i}\right )}{2}+c_{1} \sin \left (x \right )-c_2 \cos \left (x \right )-\ln \left ({\mathrm e}^{i x}-i\right )-\ln \left ({\mathrm e}^{i x}+i\right )+c_3 +\ln \left ({\mathrm e}^{i x}\right ) \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 35

DSolve[D[y[x],{x,3}]+D[y[x],x]==Tan[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\sin (x) \text {arctanh}(\sin (x))-\frac {1}{2} \log \left (\cos ^2(x)\right )-c_2 \cos (x)+c_1 \sin (x)+c_3 \]