29.11.5 problem 296

Internal problem ID [4896]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 296
Date solved : Monday, January 27, 2025 at 09:46:50 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 13

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

\[ y \left (x \right ) = -\tanh \left (-\operatorname {arctanh}\left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.699 (sec). Leaf size: 47

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

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