12.5.16 problem 12

Internal problem ID [1640]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 12
Date solved : Monday, January 27, 2025 at 05:15:35 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&=\frac {\sqrt {2}}{2} \end{align*}

✓ Solution by Maple

Time used: 0.068 (sec). Leaf size: 26

dsolve([x^2*diff(y(x),x)+2*x*y(x)=y(x)^3,y(1) = 1/2*2^(1/2)],y(x), singsol=all)
 

\[ y = \frac {\sqrt {10}\, \sqrt {4 x^{6}+x}}{8 x^{5}+2} \]

✓ Solution by Mathematica

Time used: 0.575 (sec). Leaf size: 29

DSolve[{x^2*D[y[x],x]+2*x*y[x]==y[x]^3,y[1]==1/Sqrt[2]},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt {\frac {5}{2}} \sqrt {x}}{\sqrt {4 x^5+1}} \]