10.3.1 problem 1

Internal problem ID [1166]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 1
Date solved : Monday, January 27, 2025 at 04:39:00 AM
CAS classification : [_linear]

\begin{align*} \ln \left (t \right ) y+\left (-3+t \right ) y^{\prime }&=2 t \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 57

dsolve(ln(t)*y(t)+(-3+t)*diff(y(t),t) = 2*t,y(t), singsol=all)
 

\[ y = {\mathrm e}^{\ln \left (3\right )^{2}+\operatorname {dilog}\left (\frac {t}{3}\right )} \left (-t +3\right )^{-\ln \left (3\right )} \left (-2 \left (\int t \left (-t +3\right )^{-1+\ln \left (3\right )} {\mathrm e}^{-\ln \left (3\right )^{2}-\operatorname {dilog}\left (\frac {t}{3}\right )}d t \right )+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.178 (sec). Leaf size: 69

DSolve[Log[t]*y[t]+(-3+t)*D[y[t],t] == 2*t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{\operatorname {PolyLog}\left (2,1-\frac {t}{3}\right )-\log (3) \log (t-3)} \left (\int _1^t\frac {2 e^{\log (3) \log (K[1]-3)-\operatorname {PolyLog}\left (2,1-\frac {K[1]}{3}\right )} K[1]}{K[1]-3}dK[1]+c_1\right ) \]