83.46.4 problem Ex 4 page 70

Internal problem ID [19498]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter V. Singular solutions
Problem number : Ex 4 page 70
Date solved : Monday, March 31, 2025 at 07:26:12 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.034 (sec). Leaf size: 30

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

\begin{align*} y &= -\sqrt {x}\, \left (a -x \right )+c_1 \\ y &= \sqrt {x}\, \left (a -x \right )+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 37

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

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

✓ Sympy. Time used: 0.464 (sec). Leaf size: 31

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

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