29.28.24 problem 822

Internal problem ID [5405]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 822
Date solved : Monday, January 27, 2025 at 11:21:02 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-\left (4+y^{2}\right ) y^{\prime }+4+y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.059 (sec). Leaf size: 75

dsolve(diff(y(x),x)^2-(4+y(x)^2)*diff(y(x),x)+4+y(x)^2 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -2 i \\ y \left (x \right ) &= 2 i \\ x +2 \left (\int _{}^{y \left (x \right )}\frac {1}{-\textit {\_a}^{2}+\sqrt {\textit {\_a}^{2} \left (\textit {\_a}^{2}+4\right )}-4}d \textit {\_a} \right )-c_{1} &= 0 \\ x -2 \left (\int _{}^{y \left (x \right )}\frac {1}{\textit {\_a}^{2}+\sqrt {\textit {\_a}^{2} \left (\textit {\_a}^{2}+4\right )}+4}d \textit {\_a} \right )-c_{1} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.544 (sec). Leaf size: 73

DSolve[(D[y[x],x])^2-(4+y[x]^2)*D[y[x],x]+4+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^2-4 c_1 x-1+4 c_1{}^2}{x-2 c_1} \\ y(x)\to \frac {x^2+4 c_1 x-1+4 c_1{}^2}{x+2 c_1} \\ y(x)\to -2 i \\ y(x)\to 2 i \\ \end{align*}