Internal problem ID [13051]
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. Review Exercises for chapter 1. page
136
Problem number: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {\left (1+t \right )^{2}}{\left (y+1\right )^{2}}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 5
dsolve([diff(y(t),t)= (t+1)^2/(y(t)+1)^2,y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = t \]
✓ Solution by Mathematica
Time used: 0.805 (sec). Leaf size: 16
DSolve[{y'[t]== (t+1)^2/(y[t]+1)^2,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \sqrt [3]{(t+1)^3}-1 \]