67.4.24 problem 5.3 (d)

Internal problem ID [16393]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.3 (d)
Date solved : Thursday, October 02, 2025 at 01:27:33 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+3 y&=20 x^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=10 \\ \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 15

ode:=x*diff(y(x),x)+3*y(x) = 20*x^2; 
ic:=[y(1) = 10]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {4 x^{5}+6}{x^{3}} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 16

ode=x*D[y[x],x]+3*y[x]==20*x^2; 
ic={y[1]==10}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {4 x^5+6}{x^3} \end{align*}

✓ Sympy. Time used: 0.106 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-20*x**2 + x*Derivative(y(x), x) + 3*y(x),0) 
ics = {y(1): 10} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {4 x^{5} + 6}{x^{3}} \]