83.26.11 problem 11

Internal problem ID [19264]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 11
Date solved : Monday, March 31, 2025 at 07:03:46 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

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

\[ y = \frac {x^{2}}{10}-\cos \left (\ln \left (x \right )\right ) c_2 +\sin \left (\ln \left (x \right )\right ) c_1 +c_3 \]

✓ Mathematica. Time used: 0.057 (sec). Leaf size: 28

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

\[ y(x)\to \frac {x^2}{10}-c_1 \cos (\log (x))+c_2 \sin (\log (x))+c_3 \]

✓ Sympy. Time used: 0.262 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = C_{1} + C_{2} \sin {\left (\log {\left (x \right )} \right )} + C_{3} \cos {\left (\log {\left (x \right )} \right )} + \frac {x^{2}}{10} \]