83.17.6 problem 5(a)

Internal problem ID [22052]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Examination II. page 256
Problem number : 5(a)
Date solved : Thursday, October 02, 2025 at 08:23:13 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }+y^{\prime }&=16 x^{3} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=x*diff(diff(y(x),x),x)+diff(y(x),x) = 16*x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{4}+c_1 \ln \left (x \right )+c_2 \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 16

ode=x*D[y[x],{x,2}]+D[y[x],x]==16*x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^4+c_1 \log (x)+c_2 \end{align*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-16*x**3 + x*Derivative(y(x), (x, 2)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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