Internal problem ID [11129]
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 9.
Variables searated or separable. Page 13
Problem number: Ex 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 \left (1-y^{2}\right ) x y+\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 61
dsolve(2*(1-y(x)^2)*x*y(x)+(1+x^2)*(1+y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {c_{1} x^{2}}{2}+\frac {c_{1}}{2}-\frac {\sqrt {4+\left (x^{2}+1\right )^{2} c_{1}^{2}}}{2} \\ y \left (x \right ) &= \frac {c_{1} x^{2}}{2}+\frac {c_{1}}{2}+\frac {\sqrt {4+\left (x^{2}+1\right )^{2} c_{1}^{2}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 8.437 (sec). Leaf size: 98
DSolve[2*(1-y[x]^2)*x*y[x]+(1+x^2)*(1+y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-e^{c_1} \left (x^2+1\right )-\sqrt {4+e^{2 c_1} \left (x^2+1\right )^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {4+e^{2 c_1} \left (x^2+1\right )^2}-e^{c_1} \left (x^2+1\right )\right ) \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}