29.20.26 problem 573

Internal problem ID [5167]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 573
Date solved : Monday, January 27, 2025 at 10:16:50 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.819 (sec). Leaf size: 57

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

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