56.12.3 problem Ex 3

Internal problem ID [14130]
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 19. Summary. Page 29
Problem number : Ex 3
Date solved : Thursday, October 02, 2025 at 09:15:36 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }-x^{2} y&=x^{5} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(y(x),x)-x^2*y(x) = x^5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -x^{3}-3+{\mathrm e}^{\frac {x^{3}}{3}} c_1 \]

✓ Mathematica. Time used: 0.069 (sec). Leaf size: 24

ode=D[y[x],x]-x^2*y[x]==x^5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -x^3+c_1 e^{\frac {x^3}{3}}-3 \end{align*}

✓ Sympy. Time used: 0.157 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**5 - x**2*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{\frac {x^{3}}{3}} - x^{3} - 3 \]