17.6.1 problem 1.2-1 (a)

Internal problem ID [3438]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-1, page 12
Problem number : 1.2-1 (a)
Date solved : Monday, January 27, 2025 at 07:36:43 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\left (t^{2}+1\right ) y \end{align*}

✓ 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)
 

\[ y = c_{1} {\mathrm e}^{\frac {t \left (t^{2}+3\right )}{3}} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 24

DSolve[D[y[t],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*}