Internal problem ID [14421]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Review exercises, page 80
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {t \ln \left (y\right )+\left (\frac {t^{2}}{2 y}+1\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve((t*ln(y(t)))+(t^2/(2*y(t))+1)*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{\frac {-t^{2} \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{-\frac {2 c_{1}}{t^{2}}}}{t^{2}}\right )-2 c_{1}}{t^{2}}} \]
✓ Solution by Mathematica
Time used: 1.013 (sec). Leaf size: 31
DSolve[(t*Log[y[t]])+(t^2/(2*y[t])+1)*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} t^2 W\left (\frac {2 e^{\frac {c_1}{t^2}}}{t^2}\right ) \\ y(t)\to 1 \\ \end{align*}