7.5.19 problem 19

Internal problem ID [123]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 19
Date solved : Friday, February 07, 2025 at 07:53:02 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime } x^{2}+2 x y&=5 y^{3} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 50

dsolve(x^2*diff(y(x),x)+2*x*y(x)=5*y(x)^3,y(x), singsol=all)
 

\begin{align*} y &= \frac {\sqrt {\left (c_1 \,x^{5}+2\right ) x}}{c_1 \,x^{5}+2} \\ y &= -\frac {\sqrt {\left (c_1 \,x^{5}+2\right ) x}}{c_1 \,x^{5}+2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.599 (sec). Leaf size: 51

DSolve[x^2*D[y[x],x]+2*x*y[x]==5*y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {x}}{\sqrt {2+c_1 x^5}} \\ y(x)\to \frac {\sqrt {x}}{\sqrt {2+c_1 x^5}} \\ y(x)\to 0 \\ \end{align*}