83.23.11 problem 11

Internal problem ID [19221]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter V. Singular solutions. Exercise V at page 76
Problem number : 11
Date solved : Monday, March 31, 2025 at 06:57:44 PM
CAS classification : [_quadrature]

\begin{align*} 4 x {y^{\prime }}^{2}&=\left (3 x -1\right )^{2} \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 27

ode:=4*x*diff(y(x),x)^2 = (3*x-1)^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -x^{{3}/{2}}+\sqrt {x}+c_1 \\ y &= x^{{3}/{2}}-\sqrt {x}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 34

ode=4*x*D[y[x],x]^2==(3*x-1)^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -(x-1) \sqrt {x}+c_1 \\ y(x)\to \sqrt {x} (x-1)+c_1 \\ \end{align*}

✓ Sympy. Time used: 0.409 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*Derivative(y(x), x)**2 - (3*x - 1)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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