Internal problem ID [11148]
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]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime }-2 y \left (1+x \right )-y^{\frac {5}{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 64
dsolve((1-x^2)*diff(y(x),x)-2*(1+x)*y(x)=y(x)^(5/2),y(x), singsol=all)
\[ -\frac {-1+\left (-\frac {3 \left (-1+x \right )^{3} \ln \left (-1+x \right )}{32}+\frac {3 \left (-1+x \right )^{3} \ln \left (1+x \right )}{32}+c_{1} x^{3}+\left (-3 c_{1} -\frac {3}{16}\right ) x^{2}+\left (3 c_{1} +\frac {9}{16}\right ) x -c_{1} -\frac {5}{8}\right ) y \left (x \right )^{\frac {3}{2}}}{y \left (x \right )^{\frac {3}{2}}} = 0 \]
✓ Solution by Mathematica
Time used: 1.042 (sec). Leaf size: 76
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 (32 c_1 x^3-6 x^2-96 c_1 x^2+18 x-3 (x-1)^3 \log (x-1)+3 (x-1)^3 \log (x+1)+96 c_1 x-20-32 c_1\right ){}^{2/3}} \\ y(x)\to 0 \\ \end{align*}