Internal problem ID [12950]
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 1.5 page 71
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {t}{y-2}=0} \] With initial conditions \begin {align*} [y \left (-1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 15
dsolve([diff(y(t),t)=t/(y(t)-2),y(-1) = 0],y(t), singsol=all)
\[ y \left (t \right ) = 2-\sqrt {t^{2}+3} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 21
DSolve[{y'[t]==1/(y[t]-2),{y[-1]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 2-\sqrt {2} \sqrt {t+3} \]