Internal problem ID [12571]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {t}{y-t^{2} y}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 24
dsolve([diff(y(t),t)=t/(y(t)-t^2*y(t)),y(0) = 4],y(t), singsol=all)
\[ y \left (t \right ) = \sqrt {-\ln \left (t -1\right )-\ln \left (t +1\right )+i \pi +16} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 24
DSolve[{y'[t]==t/(y[t]-t^2*y[t]),{y[0]==4}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \sqrt {-\log \left (t^2-1\right )+i \pi +16} \]