88.5.3 problem 3

Internal problem ID [23977]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 35
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:48:27 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=3 x^{2} y-3 x^{4}+2 x^{2}-2 y+2 x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=diff(y(x),x) = 3*x^2*y(x)-3*x^4+2*x^2-2*y(x)+2*x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.6 (sec). Leaf size: 21

ode=D[y[x],{x,1}]==3*x^2*y[x]-3*x^4+2*x^2-2*y[x]+2*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2+c_1 e^{x^3-2 x} \end{align*}

✓ Sympy. Time used: 0.187 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**4 - 3*x**2*y(x) - 2*x**2 - 2*x + 2*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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