Internal problem ID [1958]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.2-1, page 12
Problem number: 1.2-1 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-y \left (t^{2}+1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 15
dsolve(diff(y(t),t)=(t^2+1)*y(t),y(t), singsol=all)
\[ y \relax (t ) = c_{1} {\mathrm e}^{\frac {t \left (t^{2}+3\right )}{3}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 24
DSolve[y'[t]==(t^2+1)*y[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 e^{\frac {t^3}{3}+t} \\ y(t)\to 0 \\ \end{align*}