83.23.6 problem 6

Internal problem ID [19287]
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 : 6
Date solved : Tuesday, January 28, 2025 at 01:24:28 PM
CAS classification : [_quadrature]

\begin{align*} 4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 61

dsolve(4*x*(x-1)*(x-2)*diff(y(x),x)^2-(3*x^2-6*x+2)^2=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {\left (\int \frac {3 x^{2}-6 x +2}{\sqrt {x \left (x -1\right ) \left (x -2\right )}}d x \right )}{2}+c_{1} \\ y \left (x \right ) &= \frac {\left (\int \frac {3 x^{2}-6 x +2}{\sqrt {x \left (x -1\right ) \left (x -2\right )}}d x \right )}{2}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 53

DSolve[4*x*(x-1)*(x-2)*D[y[x],x]^2-(3*x^2-6*x+2)^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1-i \sqrt {-x \left (x^2-3 x+2\right )} \\ y(x)\to i \sqrt {-x \left (x^2-3 x+2\right )}+c_1 \\ \end{align*}