35.8.12 problem 12

Internal problem ID [6219]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 12
Date solved : Wednesday, March 05, 2025 at 12:25:21 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

\[ y = x^{2}+c_{1} \ln \left (x \right )+c_{2} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 16

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

\[ y(x)\to x^2+c_1 \log (x)+c_2 \]

✓ Sympy. Time used: 0.173 (sec). Leaf size: 12

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

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