8.4.25 problem 25

Internal problem ID [728]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 25
Date solved : Saturday, March 29, 2025 at 10:16:11 PM
CAS classification : [_linear]

\begin{align*} 3 x^{3} y+\left (x^{2}+1\right ) y^{\prime }&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 34

ode:=3*x^3*y(x)+(x^2+1)*diff(y(x),x) = 6*x/exp(3/2*x^2); 
ic:=y(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.094 (sec). Leaf size: 28

ode=3*x^3*y[x]+(x^2+1)*D[y[x],x] == 6*x/Exp[3/2*x^2]; 
ic=y[0]==1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-\frac {3 x^2}{2}} \left (3 \left (x^2+1\right )^{3/2}-2\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**3*y(x) - 6*x*exp(-3*x**2/2) + (x**2 + 1)*Derivative(y(x), x),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out