83.23.11 problem 11

Internal problem ID [19292]
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 : Tuesday, January 28, 2025 at 01:24:34 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 2.310 (sec). Leaf size: 27

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

\begin{align*} y \left (x \right ) &= -x^{{3}/{2}}+\sqrt {x}+c_{1} \\ y \left (x \right ) &= x^{{3}/{2}}-\sqrt {x}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

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

DSolve[4*x*D[y[x],x]^2==(3*x-1)^2,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*}