29.20.27 problem 574

Internal problem ID [5168]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 574
Date solved : Monday, January 27, 2025 at 10:16:54 AM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 87

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

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

✓ Solution by Mathematica

Time used: 0.506 (sec). Leaf size: 93

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

\begin{align*} y(x)\to -\sqrt {\left (x^2-1\right ) \log (1-x)-\left (x^2-1\right ) \log (x+1)+c_1 x^2-2 x-c_1} \\ y(x)\to \sqrt {\left (x^2-1\right ) \log (1-x)-\left (x^2-1\right ) \log (x+1)+c_1 x^2-2 x-c_1} \\ \end{align*}