17.7.3 problem 1.2-2 (c)

Internal problem ID [3449]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-2, page 12
Problem number : 1.2-2 (c)
Date solved : Monday, January 27, 2025 at 07:37:04 AM
CAS classification : [_linear]

\begin{align*} t y^{\prime }&=y+t^{3} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 12

dsolve([t*diff(y(t),t)=y(t)+t^3,y(1) = -2],y(t), singsol=all)
 

\[ y = \frac {\left (t^{2}-5\right ) t}{2} \]

✓ Solution by Mathematica

Time used: 0.067 (sec). Leaf size: 27

DSolve[{D[y[t],t]==y[t]+t^3,y[1]==-2},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -t^3-3 t^2-6 t+14 e^{t-1}-6 \]