8.11.36 problem 59

Internal problem ID [904]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 59
Date solved : Tuesday, March 04, 2025 at 12:00:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

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

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

\[ y = \frac {x^{2} \left (4 \ln \left (x \right ) c_1 +x^{2}+4 c_2 \right )}{4} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 26

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

\[ y(x)\to \frac {1}{4} x^2 \left (x^2+8 c_2 \log (x)+4 c_1\right ) \]

✓ Sympy. Time used: 0.233 (sec). Leaf size: 17

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

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