15.16.13 problem 13

Internal problem ID [3233]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 13
Date solved : Sunday, March 30, 2025 at 01:23:24 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-x y^{\prime }+y&=x +\ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 29

ode:=4*x^3*diff(diff(diff(y(x),x),x),x)+8*x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = x+ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x \ln \left (x \right )}{3}+\ln \left (x \right )+1-\frac {8 x}{9}+c_1 x +\frac {c_2}{\sqrt {x}}+c_3 \sqrt {x} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 40

ode=4*x^3*D[y[x],{x,3}]+8*x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==x+Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{3} (x+3) \log (x)+\frac {c_1}{\sqrt {x}}+c_2 \sqrt {x}+\left (-\frac {8}{9}+c_3\right ) x+1 \]

✓ Sympy. Time used: 0.322 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**3*Derivative(y(x), (x, 3)) + 8*x**2*Derivative(y(x), (x, 2)) - x*Derivative(y(x), x) - x + y(x) - log(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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