31.5.6 problem 12

Internal problem ID [5749]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 6
Problem number : 12
Date solved : Monday, January 27, 2025 at 01:12:32 PM
CAS classification : [_separable]

\begin{align*} \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 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ \int \frac {1}{\sqrt {f \,x^{4}+c \,x^{3}+c \,x^{2}+b x +a}}d x +\int _{}^{y \left (x \right )}\frac {1}{\sqrt {\textit {\_a}^{4} f +\textit {\_a}^{3} c +\textit {\_a}^{2} c +b \textit {\_a} +a}}d \textit {\_a} +c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 21.580 (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]*D[y[x],x]==-1,y[x],x,IncludeSingularSolutions -> True]
 

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