83.35.10 problem 10

Internal problem ID [19359]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Misc. Exercise on chapter VII. Page 118
Problem number : 10
Date solved : Monday, March 31, 2025 at 07:10:26 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} {\mathrm e}^{x} \left (x y^{\prime \prime }-y^{\prime }\right )&=x^{3} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

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

\[ y = \left (x^{2}+3 x +3\right ) {\mathrm e}^{-x}+\frac {c_1 \,x^{2}}{2}+c_2 \]

✓ Mathematica. Time used: 0.171 (sec). Leaf size: 31

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

\[ y(x)\to e^{-x} \left (x^2+3 x+3\right )+\frac {c_1 x^2}{2}+c_2 \]

✓ Sympy. Time used: 0.455 (sec). Leaf size: 27

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

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