47.1.12 problem 12

Internal problem ID [9732]
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 : 12
Date solved : Tuesday, September 30, 2025 at 06:32:25 PM
CAS classification : [_quadrature]

\begin{align*} \left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y&=0 \end{align*}

✓ Maple. Time used: 0.091 (sec). Leaf size: 55

ode:=(4*x-y(x))*diff(y(x),x)^2+6*(x-y(x))*diff(y(x),x)+2*x-5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -x +c_1 \\ y &= \frac {-4 c_1 x -\sqrt {-12 c_1 x +1}+1}{2 c_1} \\ y &= \frac {-4 c_1 x +1+\sqrt {-12 c_1 x +1}}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 51

ode=(4*x-y[x])*(D[y[x],x])^2+6*(x-y[x])*D[y[x],x]+2*x-5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -x+c_1\\ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]-4}{(K[1]-1) (K[1]+2)}dK[1]=-\log (x)+c_1,y(x)\right ] \end{align*}

✓ Sympy. Time used: 1.801 (sec). Leaf size: 48

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (4*x - y(x))*Derivative(y(x), x)**2 + (6*x - 6*y(x))*Derivative(y(x), x) - 5*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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