Internal problem ID [3897]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 6
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\frac {\sqrt {f \,x^{4}+c \,x^{3}+c \,x^{2}+b x +a}\, y^{\prime }}{\sqrt {a +b y+c y^{2}+c y^{3}+f y^{4}}}+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 56
dsolve((sqrt(a+b*x+c*x^2+c*x^3+f*x^4))/(sqrt(a+b*y(x)+c*y(x)^2+c*y(x)^3+f*y(x)^4))*diff(y(x),x)=-1,y(x), singsol=all)
\[ \int \frac {1}{\sqrt {f \,x^{4}+c \,x^{3}+c \,x^{2}+b x +a}}d x +\int _{}^{y \relax (x )}\frac {1}{\sqrt {\textit {\_a}^{4} f +\textit {\_a}^{3} c +\textit {\_a}^{2} c +b \textit {\_a} +a}}d \textit {\_a} +c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 21.514 (sec). Leaf size: 2239
DSolve[Sqrt[a+b*x+c*x^2+c*x^3+f*x^4]/Sqrt[a+b*y[x]+c*y[x]^2+c*y[x]^3+f*y[x]^4]*y'[x]==-1,y[x],x,IncludeSingularSolutions -> True]
Too large to display