83.18.4 problem 4

Internal problem ID [19135]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (A) at page 53
Problem number : 4
Date solved : Thursday, March 13, 2025 at 01:45:03 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

\begin{align*} y \left (x \right ) &= \frac {x^{2}}{2}+c_{1} \\ y \left (x \right ) &= -\frac {3 x^{2}}{2}+c_{1} \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 29

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

\begin{align*} y(x)\to -\frac {3 x^2}{2}+c_1 \\ y(x)\to \frac {x^2}{2}+c_1 \\ \end{align*}

✓ Sympy. Time used: 0.158 (sec). Leaf size: 19

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

\[ \left [ y{\left (x \right )} = C_{1} + \frac {x^{2}}{2}, \ y{\left (x \right )} = C_{1} - \frac {3 x^{2}}{2}\right ] \]