58.12.19 problem 19

Internal problem ID [14804]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number : 19
Date solved : Thursday, October 02, 2025 at 09:55:05 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y&=3 x^{4}+6 x^{3} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=x^2*diff(diff(y(x),x),x)-6*x*diff(y(x),x)+10*y(x) = 3*x^4+6*x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{3} c_1 \,x^{5}-\frac {3}{2} x^{4}-3 x^{3}+c_2 \,x^{2} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 28

ode=x^2*D[y[x],{x,2}]-6*x*D[y[x],x]+10*y[x]==3*x^4+6*x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_2 x^5-\frac {3}{2} (x+2) x^3+c_1 x^2 \end{align*}

✓ Sympy. Time used: 0.245 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**4 - 6*x**3 + x**2*Derivative(y(x), (x, 2)) - 6*x*Derivative(y(x), x) + 10*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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