89.5.17 problem 17

Internal problem ID [24367]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 17
Date solved : Thursday, October 02, 2025 at 10:22:18 PM
CAS classification : [_linear]

\begin{align*} 2 x \left (y-x^{2}\right )+y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=2*x*(y(x)-x^2)+diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{2}-1+{\mathrm e}^{-x^{2}} c_1 \]

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 20

ode=2*x*(y[x]-x^2)+D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2+c_1 e^{-x^2}-1 \end{align*}

✓ Sympy. Time used: 0.158 (sec). Leaf size: 14

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

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