73.17.40 problem 40

Internal problem ID [15503]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 40
Date solved : Monday, March 31, 2025 at 01:39:44 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 26

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

\[ y = \frac {c_2}{\sqrt {x}}+c_1 \,x^{2}+\frac {2 x^{2} \left (-2+5 \ln \left (x \right )\right )}{5} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 31

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

\[ y(x)\to 2 x^2 \log (x)+\left (-\frac {4}{5}+c_2\right ) x^2+\frac {c_1}{\sqrt {x}} \]

✓ Sympy. Time used: 0.267 (sec). Leaf size: 20

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

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