89.5.32 problem 32

Internal problem ID [24382]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 32
Date solved : Thursday, October 02, 2025 at 10:22:46 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=4 x -2 y \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 15

ode:=diff(y(x),x) = 4*x-2*y(x); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 17

ode=D[y[x],x]== 2*(2*x-y[x]); 
ic={y[0]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 x+2 e^{-2 x}-1 \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x + 2*y(x) + Derivative(y(x), x),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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