76.2.10 problem 10

Internal problem ID [17346]
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 : 10
Date solved : Tuesday, January 28, 2025 at 10:01:56 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(t*diff(y(t),t)-y(t)=t^3*exp(-t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 26

DSolve[t*D[y[t],t]-y[t]==t^3*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t \left (\int _1^te^{-K[1]} K[1]dK[1]+c_1\right ) \]