Internal problem ID [12562]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.2. page
33
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {{\mathrm e}^{t} y}{1+y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(t),t)=exp(t)*y(t)/(1+y(t)^2),y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-\frac {\operatorname {LambertW}\left ({\mathrm e}^{2 c_{1} +2 \,{\mathrm e}^{t}}\right )}{2}+c_{1} +{\mathrm e}^{t}} \]
✓ Solution by Mathematica
Time used: 33.022 (sec). Leaf size: 46
DSolve[y'[t]==Exp[t]*y[t]/(1+y[t]^2),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\sqrt {W\left (e^{2 \left (e^t+c_1\right )}\right )} y(t)\to \sqrt {W\left (e^{2 \left (e^t+c_1\right )}\right )} y(t)\to 0 \end{align*}