72.4.9 problem 16

Internal problem ID [14686]
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
Date solved : Tuesday, January 28, 2025 at 07:11:20 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {t}{y-2} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 15

dsolve([diff(y(t),t)=t/(y(t)-2),y(-1) = 0],y(t), singsol=all)
 

\[ y = 2-\sqrt {t^{2}+3} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 21

DSolve[{D[y[t],t]==1/(y[t]-2),{y[-1]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2-\sqrt {2} \sqrt {t+3} \]