40.3.29 problem 26 (c)

Internal problem ID [6633]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 26 (c)
Date solved : Sunday, March 30, 2025 at 11:12:58 AM
CAS classification : [_linear]

\begin{align*} 2 y-x^{3}+x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y = \frac {x^{5}+5 c_1}{5 x^{2}} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 19

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

\[ y(x)\to \frac {x^3}{5}+\frac {c_1}{x^2} \]

✓ Sympy. Time used: 0.204 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {C_{1} + \frac {x^{5}}{5}}{x^{2}} \]