20.3.18 problem Problem 18

Internal problem ID [3627]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 18
Date solved : Monday, January 27, 2025 at 07:47:50 AM
CAS classification : [_linear]

\begin{align*} x^{\prime }+\frac {2 x}{4-t}&=5 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 14

dsolve([diff(x(t),t)+2/(4-t)*x(t)=5,x(0) = 4],x(t), singsol=all)
 

\[ x = -t^{2}+3 t +4 \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 15

DSolve[{D[x[t],t]+2/(4-t)*x[t]==5,{x[0]==4}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to -t^2+3 t+4 \]