72.1.27 problem 30

Internal problem ID [14627]
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 : 30
Date solved : Tuesday, January 28, 2025 at 06:45:04 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.729 (sec). Leaf size: 23

dsolve([diff(y(t),t)=t/(y(t)-t^2*y(t)),y(0) = 4],y(t), singsol=all)
 

\[ y = \sqrt {i \pi -\ln \left (t -1\right )-\ln \left (t +1\right )+16} \]

✓ Solution by Mathematica

Time used: 0.089 (sec). Leaf size: 24

DSolve[{D[y[t],t]==t/(y[t]-t^2*y[t]),{y[0]==4}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \sqrt {-\log \left (t^2-1\right )+i \pi +16} \]