1.4.6 problem 6

Internal problem ID [78]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 6
Date solved : Tuesday, September 30, 2025 at 03:42:40 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (2\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 13

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

\[ y = \frac {x^{7}+32}{x^{5}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 14

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

\begin{align*} y(x)&\to \frac {x^7+32}{x^5} \end{align*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {x^{7} + 32}{x^{5}} \]