Internal problem ID [990]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+2 y x -y^{3}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (1) = \frac {\sqrt {2}}{2}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.084 (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)
\[ y \relax (x ) = \frac {\sqrt {10}\, \sqrt {4 x^{6}+x}}{8 x^{5}+2} \]
✓ Solution by Mathematica
Time used: 0.369 (sec). Leaf size: 29
DSolve[{x^2*y'[x]+2*x*y[x]==y[x]^3,y[1]==1/Sqrt[2]},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {\frac {5}{2}} \sqrt {x}}{\sqrt {4 x^5+1}} \\ \end{align*}