Internal problem ID [13058]
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: 45.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-t^{2} y-y=t^{2}+1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(t),t)=t^2*y(t)+1+y(t)+t^2,y(t), singsol=all)
\[ y \left (t \right ) = -1+{\mathrm e}^{\frac {t \left (t^{2}+3\right )}{3}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.188 (sec). Leaf size: 26
DSolve[y'[t]==t^2*y[t]+1+y[t]+t^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -1+c_1 e^{\frac {t^3}{3}+t} \\ y(t)\to -1 \\ \end{align*}