7.7.33 problem 33

Internal problem ID [211]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 33
Date solved : Wednesday, February 05, 2025 at 03:09:43 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y^{\prime }&=-\frac {3 x^{2}+2 y^{2}}{4 x y} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 47

dsolve(diff(y(x),x)=- (3*x^2+2*y(x)^2)/(4*x*y(x)),y(x), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {2}\, \sqrt {-x \left (x^{3}-2 c_1 \right )}}{2 x} \\ y &= \frac {\sqrt {2}\, \sqrt {-x \left (x^{3}-2 c_1 \right )}}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.224 (sec). Leaf size: 60

DSolve[D[y[x],x] == - (3*x^2+2*y[x]^2)/(4*x*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

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