83.48.10 problem Ex 10 page 106

Internal problem ID [19523]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VII. Exact differential equations.
Problem number : Ex 10 page 106
Date solved : Thursday, March 13, 2025 at 02:47:03 PM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} y^{\prime \prime \prime }&=x \,{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

ode:=diff(diff(diff(y(x),x),x),x) = x*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \left (-3+x \right ) {\mathrm e}^{x}+\frac {c_{1} x^{2}}{2}+c_{2} x +c_3 \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 24

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

\[ y(x)\to e^x (x-3)+x (c_3 x+c_2)+c_1 \]

✓ Sympy. Time used: 0.088 (sec). Leaf size: 20

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

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