Internal problem ID [12949]
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: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\frac {1}{\left (y+2\right )^{2}}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 13
dsolve([diff(y(t),t)=1/(y(t)+2)^2,y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \left (3 t +27\right )^{\frac {1}{3}}-2 \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 20
DSolve[{y'[t]==1/(y[t]+2)^2,{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \sqrt [3]{3} \sqrt [3]{t+9}-2 \]