78.1.6 problem 1.f

Internal problem ID [20932]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 1, First order ODEs. Problems section 1.5
Problem number : 1.f
Date solved : Thursday, October 02, 2025 at 06:49:28 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }-2 y&=x^{2} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.026 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to x^2 (\log (x)+1) \end{align*}

✓ Sympy. Time used: 0.108 (sec). Leaf size: 10

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

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