Internal problem ID [14434]
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: 32.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {{\mathrm e}^{t y} y+t \,{\mathrm e}^{t y} y^{\prime }=2 t} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 14
dsolve([(y(t)*exp(t*y(t))-2*t)+(t*exp(t*y(t)))*diff(y(t),t)=0,y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\ln \left (t^{2}+1\right )}{t} \]
✓ Solution by Mathematica
Time used: 0.498 (sec). Leaf size: 15
DSolve[{(y[t]*Exp[t*y[t]]-2*t)+(t*Exp[t*y[t]])*y'[t]==0,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {\log \left (t^2+1\right )}{t} \]