8.11.37 problem 60

Internal problem ID [905]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 60
Date solved : Saturday, March 29, 2025 at 10:34:04 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y&=8 x^{{4}/{3}} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 20

ode:=4*x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+3*y(x) = 8*x^(4/3); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sqrt {x}\, c_2 +x^{{3}/{2}} c_1 -\frac {72 x^{{4}/{3}}}{5} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 31

ode=4*x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+3*y[x]==8*x^(4/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{5} \sqrt {x} \left (-72 x^{5/6}+5 c_2 x+5 c_1\right ) \]

✓ Sympy. Time used: 0.368 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x**(4/3) + 4*x**2*Derivative(y(x), (x, 2)) - 4*x*Derivative(y(x), x) + 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sqrt {x} + C_{2} x^{\frac {3}{2}} - \frac {72 x^{\frac {4}{3}}}{5} \]