Internal problem ID [521]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.4. Page 76
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y+\ln \left (t \right ) y^{\prime }=\cot \left (t \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 32
dsolve(y(t)+ln(t)*diff(y(t),t) = cot(t),y(t), singsol=all)
\[ y \left (t \right ) = \left (\int \frac {\cot \left (t \right ) {\mathrm e}^{-\operatorname {expIntegral}_{1}\left (-\ln \left (t \right )\right )}}{\ln \left (t \right )}d t +c_{1} \right ) {\mathrm e}^{\operatorname {expIntegral}_{1}\left (-\ln \left (t \right )\right )} \]
✓ Solution by Mathematica
Time used: 0.142 (sec). Leaf size: 36
DSolve[y[t]+Log[t]*y'[t] == Cot[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-\operatorname {LogIntegral}(t)} \left (\int _1^t\frac {e^{\operatorname {LogIntegral}(K[1])} \cot (K[1])}{\log (K[1])}dK[1]+c_1\right ) \]