73.17.7 problem 7

Internal problem ID [15470]
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 : 7
Date solved : Monday, March 31, 2025 at 01:38:49 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = \frac {\sqrt {x}\, \left (x +6 c_1 \right )}{3}+c_2 \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 23

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

\[ y(x)\to \frac {1}{3} \sqrt {x} (x+6 c_1)+c_2 \]

✓ Sympy. Time used: 0.296 (sec). Leaf size: 17

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

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