83.46.4 problem Ex 4 page 70

Internal problem ID [19569]
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 : Tuesday, January 28, 2025 at 01:57:16 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 30

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

\begin{align*} y \left (x \right ) &= -\sqrt {x}\, \left (a -x \right )+c_{1} \\ y \left (x \right ) &= \sqrt {x}\, \left (a -x \right )+c_{1} \\ \end{align*}

✓ Solution by Mathematica

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

DSolve[4*x*D[y[x],x]^2==(3*x-a)^2,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*}