47.1.6 problem 6

Internal problem ID [9726]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 94. Factoring the left member. EXERCISES Page 309
Problem number : 6
Date solved : Tuesday, September 30, 2025 at 06:32:22 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=diff(y(x),x)^2-(x^2*y(x)+3)*diff(y(x),x)+3*x^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= c_1 \,{\mathrm e}^{\frac {x^{3}}{3}} \\ y &= 3 x +c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 27

ode=(D[y[x],x])^2-(x^2*y[x]+3)*D[y[x],x]+3*x^2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{\frac {x^3}{3}}\\ y(x)&\to 3 x+c_1 \end{align*}

✓ Sympy. Time used: 0.199 (sec). Leaf size: 17

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

\[ \left [ y{\left (x \right )} = C_{1} + 3 x, \ y{\left (x \right )} = C_{1} e^{\frac {x^{3}}{3}}\right ] \]