Internal problem ID [1001]
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: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y y^{\prime } x +x^{2}+y^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 18
dsolve([x*y(x)*diff(y(x),x)+x^2+y(x)^2=0,y(1) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {\sqrt {-2 x^{4}+18}}{2 x} \]
✓ Solution by Mathematica
Time used: 0.209 (sec). Leaf size: 25
DSolve[{x*y[x]*y'[x]+x^2+y[x]^2==0,y[1]==2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {9-x^4}}{\sqrt {2} x} \\ \end{align*}