1.4.25 problem 25

Internal problem ID [97]
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 1.5 (linear equations). Problems at page 54
Problem number : 25
Date solved : Tuesday, September 30, 2025 at 03:43:15 AM
CAS classification : [_linear]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+3 x^{3} y&=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: 0.049 (sec). Leaf size: 34

ode:=(x^2+1)*diff(y(x),x)+3*x^3*y(x) = 6*x*exp(-3/2*x^2); 
ic:=[y(0) = 1]; 
dsolve([ode,op(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: 0.062 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to e^{-\frac {3 x^2}{2}} \left (3 \left (x^2+1\right )^{3/2}-2\right ) \end{align*}

✗ 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