7.3.22 problem 22

Internal problem ID [62]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 22
Date solved : Tuesday, March 04, 2025 at 10:41:15 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=-3 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 18

ode:=diff(y(x),x) = 4*x^3*y(x)-y(x); 
ic:=y(1) = -3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -3 \,{\mathrm e}^{x \left (x -1\right ) \left (x^{2}+x +1\right )} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 16

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

\[ y(x)\to -3 e^{x^4-x} \]

✓ Sympy. Time used: 0.344 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**3*y(x) + y(x) + Derivative(y(x), x),0) 
ics = {y(1): -3} 
dsolve(ode,func=y(x),ics=ics)
 

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