66.1.31 problem Problem 45

Internal problem ID [13878]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 45
Date solved : Tuesday, January 28, 2025 at 06:07:03 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} x^{\prime }+5 x&=10 t +2 \end{align*}

With initial conditions

\begin{align*} x \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 7

dsolve([diff(x(t),t)+5*x(t)=10*t+2,x(1) = 2],x(t), singsol=all)
 

\[ x \left (t \right ) = 2 t \]

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 8

DSolve[{D[x[t],t]+5*x[t]==10*t+2,{x[1]==2}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 2 t \]