41.1.27 problem 27

Internal problem ID [8694]
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 : 27
Date solved : Tuesday, September 30, 2025 at 05:41:35 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=2 x -3 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=diff(y(x),x)-y(x) = 2*x-3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -2 x +1+{\mathrm e}^{x} c_1 \]

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 32

ode=D[y[x],x]-y[x]==2*x-3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^x \left (\int _1^xe^{-K[1]} (2 K[1]-3)dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.066 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x - y(x) + Derivative(y(x), x) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x} - 2 x + 1 \]