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]
Solve \begin {gather*} \boxed {y+\ln \relax (t ) y^{\prime }-\cot \relax (t )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(y(t)+ln(t)*diff(y(t),t) = cot(t),y(t), singsol=all)
\[ y \relax (t ) = \left (\int \frac {\cot \relax (t ) {\mathrm e}^{-\expIntegral \left (1, -\ln \relax (t )\right )}}{\ln \relax (t )}d t +c_{1}\right ) {\mathrm e}^{\expIntegral \left (1, -\ln \relax (t )\right )} \]
✓ Solution by Mathematica
Time used: 0.138 (sec). Leaf size: 36
DSolve[y[t]+Log[t]*y'[t] == Cot[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-\text {LogIntegral}(t)} \left (\int _1^t\frac {e^{\text {LogIntegral}(K[1])} \cot (K[1])}{\log (K[1])}dK[1]+c_1\right ) \\ \end{align*}