63.1.13 problem 13

Internal problem ID [15453]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 13
Date solved : Thursday, October 02, 2025 at 10:15:00 AM
CAS classification : [_separable]

\begin{align*} y-a +x^{2} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.176 (sec). Leaf size: 10

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

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