69.1.68 problem 96

Internal problem ID [14150]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 96
Date solved : Monday, March 31, 2025 at 12:10:51 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

ode:=y(x) = x*diff(y(x),x)+diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \left (x +1\right ) \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 16

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

\begin{align*} y(x)\to c_1 (x+1) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.213 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = C_{1} \left (x + 1\right ) \]