Internal problem ID [516]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.4. Page 76
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\ln \relax (t ) y+\left (t -3\right ) y^{\prime }-2 t=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 56
dsolve(ln(t)*y(t)+(-3+t)*diff(y(t),t) = 2*t,y(t), singsol=all)
\[ y \relax (t ) = 3^{-\ln \left (3-t \right )} \left (\int -2 t \left (3-t \right )^{-1+\ln \relax (3)} {\mathrm e}^{-\ln \relax (3)^{2}} {\mathrm e}^{-\dilog \left (\frac {t}{3}\right )}d t +c_{1}\right ) {\mathrm e}^{\ln \relax (3)^{2}} {\mathrm e}^{\dilog \left (\frac {t}{3}\right )} \]
✓ Solution by Mathematica
Time used: 0.202 (sec). Leaf size: 69
DSolve[Log[t]*y[t]+(-3+t)*y'[t] == 2*t,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{\text {PolyLog}\left (2,1-\frac {t}{3}\right )-\log (3) \log (t-3)} \left (\int _1^t\frac {2 e^{\log (3) \log (K[1]-3)-\text {PolyLog}\left (2,1-\frac {K[1]}{3}\right )} K[1]}{K[1]-3}dK[1]+c_1\right ) \\ \end{align*}