63.1.33 problem 50

Internal problem ID [15473]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 50
Date solved : Thursday, October 02, 2025 at 10:16:55 AM
CAS classification : [_linear]

\begin{align*} x +2 y+1-\left (2 x -3\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=x+2*y(x)+1-(2*x-3)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {5}{4}+\frac {\left (2 x -3\right ) \ln \left (2 x -3\right )}{4}+\left (2 x -3\right ) c_1 \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 35

ode=(x+2*y[x]+1)-(2*x-3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to (2 x-3) \left (\frac {x+1}{6-4 x}+\frac {1}{4} \log (6-4 x)+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.207 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x - (2*x - 3)*Derivative(y(x), x) + 2*y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 C_{1} x - 3 C_{1} + \frac {x \log {\left (2 x - 3 \right )}}{2} - \frac {3 \log {\left (2 x - 3 \right )}}{4} - \frac {5}{4} \]