69.2.4 problem 24

Internal problem ID [17968]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 2. The method of isoclines. Exercises page 27
Problem number : 24
Date solved : Thursday, October 02, 2025 at 02:31:37 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(x),x) = 1/2*x-y(x)+3/2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 20

ode=D[y[x],x]==1/2*(x-2*y[x]+3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x}{2}+c_1 e^{-x}+1 \end{align*}

✓ Sympy. Time used: 0.071 (sec). Leaf size: 12

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

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