83.46.5 problem Ex 5 page 70

Internal problem ID [19570]
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 5 page 70
Date solved : Tuesday, January 28, 2025 at 01:57:17 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.044 (sec). Leaf size: 85

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

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

✓ Solution by Mathematica

Time used: 0.157 (sec). Leaf size: 55

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

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