Internal problem ID [14344]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
\[ \boxed {y^{\prime }-\frac {y}{2}-\frac {t}{y}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(diff(y(t),t)-1/2*y(t)=t/y(t),y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \sqrt {{\mathrm e}^{t} c_{1} -2 t -2} \\ y \left (t \right ) &= -\sqrt {{\mathrm e}^{t} c_{1} -2 t -2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.39 (sec). Leaf size: 41
DSolve[y'[t]-1/2*y[t]==t/y[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\sqrt {-2 t+c_1 e^t-2} \\ y(t)\to \sqrt {-2 t+c_1 e^t-2} \\ \end{align*}