Internal problem ID [6039]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 97. The p-discriminant equation. EXERCISES
Page 314
Problem number: 14.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational]
Solve \begin {gather*} \boxed {4 y^{3} \left (y^{\prime }\right )^{2}+4 x y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.406 (sec). Leaf size: 287
dsolve(4*y(x)^3*diff(y(x),x)^2+4*x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ \int _{\textit {\_b}}^{x}\frac {-2 \textit {\_a} +\sqrt {-y \relax (x )^{4}+\textit {\_a}^{2}}}{2 y \relax (x )^{4}+6 \textit {\_a}^{2}}d \textit {\_a} +\int _{}^{y \relax (x )}\left (\frac {\textit {\_f}^{3}}{-\textit {\_f}^{4}+\sqrt {-\textit {\_f}^{4}+x^{2}}\, x -x^{2}}-\left (\int _{\textit {\_b}}^{x}\left (-\frac {\textit {\_f}^{3}}{\sqrt {-\textit {\_f}^{4}+\textit {\_a}^{2}}\, \left (\textit {\_f}^{4}+3 \textit {\_a}^{2}\right )}-\frac {2 \left (-2 \textit {\_a} +\sqrt {-\textit {\_f}^{4}+\textit {\_a}^{2}}\right ) \textit {\_f}^{3}}{\left (\textit {\_f}^{4}+3 \textit {\_a}^{2}\right )^{2}}\right )d \textit {\_a} \right )\right )d \textit {\_f} +c_{1} = 0 \\ \int _{\textit {\_b}}^{x}-\frac {2 \textit {\_a} +\sqrt {-y \relax (x )^{4}+\textit {\_a}^{2}}}{2 \left (y \relax (x )^{4}+3 \textit {\_a}^{2}\right )}d \textit {\_a} +\int _{}^{y \relax (x )}\left (-\frac {\textit {\_f}^{3}}{\textit {\_f}^{4}+\sqrt {-\textit {\_f}^{4}+x^{2}}\, x +x^{2}}-\left (\int _{\textit {\_b}}^{x}\left (\frac {\textit {\_f}^{3}}{\sqrt {-\textit {\_f}^{4}+\textit {\_a}^{2}}\, \left (\textit {\_f}^{4}+3 \textit {\_a}^{2}\right )}+\frac {2 \left (2 \textit {\_a} +\sqrt {-\textit {\_f}^{4}+\textit {\_a}^{2}}\right ) \textit {\_f}^{3}}{\left (\textit {\_f}^{4}+3 \textit {\_a}^{2}\right )^{2}}\right )d \textit {\_a} \right )\right )d \textit {\_f} +c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.464 (sec). Leaf size: 2815
DSolve[4*y[x]^3*(y'[x])^2+4*x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
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