Internal problem ID [10134]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 14. Equations
reducible to linear equations (Bernoulli). Page 21
Problem number: Ex 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {\left (-x^{2}+1\right ) y^{\prime }-2 \left (x +1\right ) y-y^{\frac {5}{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve((1-x^2)*diff(y(x),x)-2*(1+x)*y(x)=y(x)^(5/2),y(x), singsol=all)
\[ \frac {1}{y \relax (x )^{\frac {3}{2}}}-\left (-\frac {1}{4 \left (x -1\right )^{3}}+\frac {3}{16 \left (x -1\right )^{2}}-\frac {3}{16 \left (x -1\right )}-\frac {3 \ln \left (x -1\right )}{32}+\frac {3 \ln \left (1+x \right )}{32}+c_{1}\right ) \left (x -1\right )^{3} = 0 \]
✓ Solution by Mathematica
Time used: 0.703 (sec). Leaf size: 65
DSolve[(1-x^2)*y'[x]-2*(1+x)*y[x]==y[x]^(5/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {8 \sqrt [3]{2}}{\left (2 \left (-3 x^2+9 x+16 c_1 (x-1)^3-10\right )-3 (x-1)^3 \log (x-1)+3 (x-1)^3 \log (x+1)\right ){}^{2/3}} \\ y(x)\to 0 \\ \end{align*}