18.1.10 problem Problem 14.6

Internal problem ID [3466]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number : Problem 14.6
Date solved : Monday, January 27, 2025 at 07:37:57 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} y^{\prime }&=-\frac {2 x^{2}+y^{2}+x}{y x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 49

dsolve(diff(y(x),x) = - (2*x^2+y(x)^2+x)/(x*y(x)),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-9 x^{4}-6 x^{3}+9 c_{1}}}{3 x} \\ y \left (x \right ) &= \frac {\sqrt {-9 x^{4}-6 x^{3}+9 c_{1}}}{3 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.281 (sec). Leaf size: 56

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

\begin{align*} y(x)\to -\frac {\sqrt {-x^4-\frac {2 x^3}{3}+c_1}}{x} \\ y(x)\to \frac {\sqrt {-x^4-\frac {2 x^3}{3}+c_1}}{x} \\ \end{align*}