Internal problem ID [13828]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+y \sec \left (t \right )=t} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 59
dsolve([diff(y(t),t)+y(t)*sec(t)=t,y(0) = 0],y(t), singsol=all)
\[ y = \frac {i \pi ^{2}+12 i t^{2}-48 t \ln \left (1+i {\mathrm e}^{i t}\right )+48 i \operatorname {polylog}\left (2, -i {\mathrm e}^{i t}\right )-48 \operatorname {Catalan}}{24 \sec \left (t \right )+24 \tan \left (t \right )} \]
✓ Solution by Mathematica
Time used: 0.209 (sec). Leaf size: 146
DSolve[{y'[t]+y[t]*Sec[t]==t,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{24} e^{-2 \text {arctanh}\left (\tan \left (\frac {t}{2}\right )\right )} \left (-48 C+48 i \operatorname {PolyLog}\left (2,-i e^{i t}\right )+12 i t^2-36 i \pi t-48 t \log \left (1+i e^{i t}\right )-48 \pi \log \left (1+e^{-i t}\right )+24 \pi \log \left (1+i e^{i t}\right )+48 \pi \log \left (\cos \left (\frac {t}{2}\right )\right )-24 \pi \log \left (-\cos \left (\frac {1}{4} (2 t+\pi )\right )\right )+25 i \pi ^2+36 \pi \log (2)-24 \pi \log (1+i)\right ) \]