67.15.78 problem 22.15 (e)

Internal problem ID [16796]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.15 (e)
Date solved : Thursday, October 02, 2025 at 01:39:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y&=4 x^{3} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 21

ode:=3*x^2*diff(diff(y(x),x),x)-7*x*diff(y(x),x)+3*y(x) = 4*x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{{1}/{3}} c_2 +\left (c_1 +\frac {\ln \left (x \right )}{2}-\frac {3}{16}\right ) x^{3} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 33

ode=3*x^2*D[y[x],{x,2}]-7*x*D[y[x],x]+3*y[x]==4*x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} x^3 \log (x)+\left (-\frac {3}{16}+c_2\right ) x^3+c_1 \sqrt [3]{x} \end{align*}

✓ Sympy. Time used: 0.169 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**3 + 3*x**2*Derivative(y(x), (x, 2)) - 7*x*Derivative(y(x), x) + 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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