56.6.5 problem Ex 5

Internal problem ID [14104]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 13. Linear equations of first order. Page 19
Problem number : Ex 5
Date solved : Thursday, October 02, 2025 at 09:13:44 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = x^{2} \left ({\mathrm e}^{\frac {1}{x}} c_1 +1\right ) \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.174 (sec). Leaf size: 14

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

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