74.8.19 problem 19

Internal problem ID [16155]
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
Date solved : Tuesday, January 28, 2025 at 08:53:00 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} t \ln \left (y\right )+\left (\frac {t^{2}}{2 y}+1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 31

dsolve((t*ln(y(t)))+(t^2/(2*y(t))+1)*diff(y(t),t)=0,y(t), singsol=all)
 

\[ y = {\mathrm e}^{\frac {-t^{2} \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{-\frac {2 c_{1}}{t^{2}}}}{t^{2}}\right )-2 c_{1}}{t^{2}}} \]

✓ Solution by Mathematica

Time used: 0.965 (sec). Leaf size: 31

DSolve[(t*Log[y[t]])+(t^2/(2*y[t])+1)*D[y[t],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*}