8.5.19 problem 19

Internal problem ID [747]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 19
Date solved : Monday, January 27, 2025 at 03:02:24 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 50

dsolve(2*x*y(x)+x^2*diff(y(x),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: 0.505 (sec). Leaf size: 51

DSolve[2*x*y[x]+x^2*D[y[x],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*}