40.7.6 problem 15

Internal problem ID [6696]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 12. Linear equations of order n. Supplemetary problems. Page 81
Problem number : 15
Date solved : Sunday, March 30, 2025 at 11:19:59 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime \prime }+x y^{\prime }-y&=3 x^{4} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

ode:=x^3*diff(diff(diff(y(x),x),x),x)+x*diff(y(x),x)-y(x) = 3*x^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x \left (9 c_3 \ln \left (x \right )^{2}+x^{3}+9 c_2 \ln \left (x \right )+9 c_1 \right )}{9} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 31

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

\[ y(x)\to \frac {x^4}{9}+c_1 x+c_3 x \log ^2(x)+c_2 x \log (x) \]

✓ Sympy. Time used: 0.353 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = x \left (C_{1} + C_{2} \log {\left (x \right )} + C_{3} \log {\left (x \right )}^{2} + \frac {x^{3}}{9}\right ) \]