Internal problem ID [13048]
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: 33.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-t^{2} y^{3}-y^{3}=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = -{\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 18
dsolve([diff(y(t),t)= t^2*y(t)^3+y(t)^3,y(0) = -1/2],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {3}{\sqrt {-6 t^{3}-18 t +36}} \]
✓ Solution by Mathematica
Time used: 0.319 (sec). Leaf size: 28
DSolve[{y'[t]==t^2*y[t]^3+y[t]^3,{y[0]==-1/2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {\sqrt {\frac {3}{2}}}{\sqrt {-t^3-3 t+6}} \]