82.11.4 problem Ex. 4

Internal problem ID [18764]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 28
Problem number : Ex. 4
Date solved : Tuesday, January 28, 2025 at 12:15:36 PM
CAS classification : [_rational, _Bernoulli]

\begin{align*} y^{\prime }+\frac {x y}{-x^{2}+1}&=x \sqrt {y} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

dsolve(diff(y(x),x)+x*y(x)/(1-x^2)=x*y(x)^(1/2),y(x), singsol=all)
 

\[ \sqrt {y \left (x \right )}+\frac {1}{3}-\frac {x^{2}}{3}-\left (x -1\right )^{{1}/{4}} \left (x +1\right )^{{1}/{4}} c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.226 (sec). Leaf size: 29

DSolve[D[y[x],x]+x*y[x]/(1-x^2)==x*y[x]^(1/2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{9} \left (x^2+3 c_1 \sqrt [4]{x^2-1}-1\right ){}^2 \]