87.18.13 problem 13

Internal problem ID [23654]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 135
Problem number : 13
Date solved : Thursday, October 02, 2025 at 09:43:52 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 5 x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y&=\sqrt {x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 18

ode:=5*x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)+3*y(x) = x^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 x +x^{{3}/{5}} c_1 +4 \sqrt {x} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 25

ode=5*x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+3*y[x]==Sqrt[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 x^{3/5}+4 \sqrt {x}+c_2 x \end{align*}

✓ Sympy. Time used: 0.223 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(x) + 5*x**2*Derivative(y(x), (x, 2)) - 3*x*Derivative(y(x), x) + 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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