10.1.19 problem 19

Internal problem ID [1116]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 19
Date solved : Monday, January 27, 2025 at 04:33:58 AM
CAS classification : [_linear]

\begin{align*} 4 t^{2} y+t^{3} y^{\prime }&={\mathrm e}^{-t} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 16

dsolve([4*t^2*y(t)+t^3*diff(y(t),t) = exp(-t),y(-1) = 0],y(t), singsol=all)
 

\[ y = -\frac {\left (t +1\right ) {\mathrm e}^{-t}}{t^{4}} \]

✓ Solution by Mathematica

Time used: 0.076 (sec). Leaf size: 18

DSolve[{4*t^2*y[t]+t^3*D[y[t],t] == Exp[-t],y[-1]==0},y[t],t,IncludeSingularSolutions -> True]
 

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