85.22.3 problem 5

Internal problem ID [22575]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 55
Problem number : 5
Date solved : Thursday, October 02, 2025 at 08:51:59 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\[ y = \frac {1}{4} c_1 \,x^{4}-\frac {4}{3} x^{3}+c_2 \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \frac {c_1 x^4}{4}-\frac {4 x^3}{3}+c_2 \end{align*}

✓ Sympy. Time used: 0.178 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = C_{1} + C_{2} x^{4} - \frac {4 x^{3}}{3} \]