Internal problem ID [3552]
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]
\[ \boxed {{y^{\prime }}^{2}-\left (4+y^{2}\right ) y^{\prime }+4+y^{2}=0} \]
✓ 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: 0.453 (sec). Leaf size: 55
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 x+\frac {1}{-x+2 c_1}-2 c_1 \\ y(x)\to x-\frac {1}{x+2 c_1}+2 c_1 \\ y(x)\to -2 i \\ y(x)\to 2 i \\ \end{align*}