85.64.11 problem 2

Internal problem ID [22878]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 213
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:16:09 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} 3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=1+x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 27

ode:=x^3*diff(diff(diff(y(x),x),x),x)+3*x^2*diff(diff(y(x),x),x) = 1+x; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 34

ode=x^3*D[y[x],{x,3}]+3*x^2*D[y[x],{x,2}]==1+x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \left ((x-2) \log (x)+\frac {c_1}{x}+(-1+2 c_3) x+2 c_2\right ) \end{align*}

✓ Sympy. Time used: 0.150 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) + 3*x**2*Derivative(y(x), (x, 2)) - x - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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