29.21.4 problem 580

Internal problem ID [5174]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 580
Date solved : Monday, January 27, 2025 at 10:17:39 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 42

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

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

✓ Solution by Mathematica

Time used: 0.883 (sec). Leaf size: 115

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

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