75.8.3 problem 201

Internal problem ID [16748]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 8. First order not solved for the derivative. Exercises page 67
Problem number : 201
Date solved : Monday, March 31, 2025 at 03:15:46 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-2 x y^{\prime }-8 x^{2}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=diff(y(x),x)^2-2*x*diff(y(x),x)-8*x^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 2 x^{2}+c_1 \\ y &= -x^{2}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 25

ode=D[y[x],x]^2-2*x*D[y[x],x]-8*x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.158 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x**2 - 2*x*Derivative(y(x), x) + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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