83.5.9 problem 9

Internal problem ID [19025]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (D) at page 16
Problem number : 9
Date solved : Thursday, March 13, 2025 at 01:23:40 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+3 x^{2} y&=x^{5} {\mathrm e}^{x^{3}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=diff(y(x),x)+3*x^2*y(x) = x^5*exp(x^3); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {x^{3} {\mathrm e}^{x^{3}}}{6}-\frac {{\mathrm e}^{x^{3}}}{12}+{\mathrm e}^{-x^{3}} c_{1} \]

✓ Mathematica. Time used: 0.104 (sec). Leaf size: 32

ode=D[y[x],x]+3*x^2*y[x]==x^5*Exp[x^3]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{12} e^{x^3} \left (2 x^3-1\right )+c_1 e^{-x^3} \]

✓ Sympy. Time used: 0.373 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**5*exp(x**3) + 3*x**2*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x^{3}} + \frac {x^{3} e^{x^{3}}}{6} - \frac {e^{x^{3}}}{12} \]