76.15.32 problem 33

Internal problem ID [17594]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.5 (Nonhomogeneous Equations, Method of Undetermined Coefficients). Problems at page 260
Problem number : 33
Date solved : Thursday, March 13, 2025 at 10:37:27 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y&=x \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=x^2*diff(diff(y(x),x),x)+7*x*diff(y(x),x)+5*y(x) = x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{6}+3 c_{1} x^{4}-4 c_{1}^{3}+12 c_{2}}{12 x^{5}} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 23

ode=x^2*D[y[x],{x,2}]+7*x*D[y[x],x]+5*y[x]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_1}{x^5}+\frac {x}{12}+\frac {c_2}{x} \]

✓ Sympy. Time used: 0.213 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 7*x*Derivative(y(x), x) - x + 5*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{5}} + \frac {C_{2}}{x} + \frac {x}{12} \]