76.2.19 problem 19

Internal problem ID [17355]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 10:02:13 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 16

dsolve([t^3*diff(y(t),t)+4*t^2*y(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: 0.079 (sec). Leaf size: 25

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

\[ y(t)\to \frac {\int _{-1}^te^{-K[1]} K[1]dK[1]}{t^4} \]