83.30.5 problem 5

Internal problem ID [19313]
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. Exercise VII (D) at page 109
Problem number : 5
Date solved : Monday, March 31, 2025 at 07:06:36 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime \prime }-4 x y^{\prime \prime }+6 y^{\prime }&=4 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=x^2*diff(diff(diff(y(x),x),x),x)-4*x*diff(diff(y(x),x),x)+6*diff(y(x),x) = 4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{4} c_1 \,x^{4}+\frac {1}{3} c_2 \,x^{3}+\frac {2}{3} x +c_3 \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 31

ode=x^2*D[y[x],{x,3}]-4*x*D[y[x],{x,2}]+6*D[y[x],x]==4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_2 x^4}{4}+\frac {c_1 x^3}{3}+\frac {2 x}{3}+c_3 \]

✓ Sympy. Time used: 0.328 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 3)) - 4*x*Derivative(y(x), (x, 2)) + 6*Derivative(y(x), x) - 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x^{3} + C_{3} x^{4} + \frac {2 x}{3} \]