Internal problem ID [13827]
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: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {2 y^{\prime }+t y=\ln \left (t \right )} \] With initial conditions \begin {align*} [y \left ({\mathrm e}\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve([2*diff(y(t),t)+t*y(t)=ln(t),y(exp(1)) = 0],y(t), singsol=all)
\[ y = \frac {\left (\int _{{\mathrm e}}^{t}\ln \left (\textit {\_z1} \right ) {\mathrm e}^{\frac {\textit {\_z1}^{2}}{4}}d \textit {\_z1} \right ) {\mathrm e}^{-\frac {t^{2}}{4}}}{2} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 95
DSolve[{2*y'[t]+t*y[t]==Log[t],{y[Exp[1]]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-\frac {t^2}{4}} \left (-t \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};\frac {t^2}{4}\right )+e \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};\frac {e^2}{4}\right )+\sqrt {\pi } \text {erfi}\left (\frac {t}{2}\right ) \log (t)-\sqrt {\pi } \text {erfi}\left (\frac {e}{2}\right )\right ) \]