17.7.6 problem 1.2-2 (f)

Internal problem ID [3452]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-2, page 12
Problem number : 1.2-2 (f)
Date solved : Monday, January 27, 2025 at 07:37:11 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: 0.009 (sec). Leaf size: 14

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

\[ y = \frac {t^{4}+7}{4 t} \]

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 27

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

\[ y(t)\to t^3-3 t^2+6 t+4 e^{1-t}-6 \]