28.1.71 problem 74

Internal problem ID [4377]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 74
Date solved : Monday, January 27, 2025 at 09:09:37 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} y \left (6 y^{2}-x -1\right )+2 x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 54

dsolve(y(x)*(6*y(x)^2-x-1)+2*x*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left ({\mathrm e}^{-x} c_{1} +6\right ) x}}{{\mathrm e}^{-x} c_{1} +6} \\ y \left (x \right ) &= -\frac {\sqrt {\left ({\mathrm e}^{-x} c_{1} +6\right ) x}}{{\mathrm e}^{-x} c_{1} +6} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.686 (sec). Leaf size: 65

DSolve[y[x]*(6*y[x]^2-x-1)+2*x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {e^{x/2} \sqrt {x}}{\sqrt {6 e^x+c_1}} \\ y(x)\to \frac {e^{x/2} \sqrt {x}}{\sqrt {6 e^x+c_1}} \\ y(x)\to 0 \\ \end{align*}