47.1.25 problem 25

Internal problem ID [7406]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number : 25
Date solved : Monday, January 27, 2025 at 02:53:09 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }+t&=1 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 12

dsolve(diff(x(t),t)+t=1,x(t), singsol=all)
 

\[ x \left (t \right ) = -\frac {1}{2} t^{2}+t +c_{1} \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 16

DSolve[D[x[t],t]+t==1,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to -\frac {t^2}{2}+t+c_1 \]