Internal problem ID [12628]
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: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {1}{\left (y+1\right ) \left (-2+t \right )}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 24
dsolve([diff(y(t),t)=1/( (y(t)+1)*(t-2)),y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -1+\sqrt {1+2 \ln \left (t -2\right )-2 \ln \left (2\right )-2 i \pi } \]
✓ Solution by Mathematica
Time used: 0.188 (sec). Leaf size: 28
DSolve[{y'[t]==1/( (y[t]+1)*(t-2)),{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -1+\sqrt {2 \log (t-2)-2 i \pi +1-\log (4)} \]