15.6.11 problem 11

Internal problem ID [2968]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 11
Date solved : Sunday, March 30, 2025 at 01:02:31 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=5 y+x +1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=x*diff(y(x),x) = 5*y(x)+x+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {1}{4} x -\frac {1}{5}+c_1 \,x^{5} \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 20

ode=x*D[y[x],x]==5*y[x]+x+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 x^5-\frac {x}{4}-\frac {1}{5} \]

✓ Sympy. Time used: 0.251 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - x - 5*y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x^{5} - \frac {x}{4} - \frac {1}{5} \]