Internal problem ID [4061]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 28
Problem number: 822.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}-\left (4+y^{2}\right ) y^{\prime }+y^{2}=-4} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 83
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 -\left (\int _{}^{y \left (x \right )}\frac {1}{2+\frac {\textit {\_a}^{2}}{2}-\frac {\sqrt {\textit {\_a}^{2} \left (\textit {\_a}^{2}+4\right )}}{2}}d \textit {\_a} \right )-c_{1} = 0 x -\left (\int _{}^{y \left (x \right )}\frac {1}{2+\frac {\textit {\_a}^{2}}{2}+\frac {\sqrt {\textit {\_a}^{2} \left (\textit {\_a}^{2}+4\right )}}{2}}d \textit {\_a} \right )-c_{1} = 0 \end{align*}
✓ Solution by Mathematica
Time used: 0.463 (sec). Leaf size: 73
DSolve[(y'[x])^2-(4+y[x]^2)y'[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*}