29.8.31 problem 236

Internal problem ID [4836]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 236
Date solved : Sunday, March 30, 2025 at 04:02:57 AM
CAS classification : [_linear]

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

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

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

\[ y = \frac {2 x^{3}}{7}+\frac {c_1}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 21

ode=2 x D[y[x],x]==2 x^3-y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {2 x^3}{7}+\frac {c_1}{\sqrt {x}} \]

✓ Sympy. Time used: 0.178 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \frac {C_{1}}{\sqrt {x}} + \frac {2 x^{3}}{7} \]