Internal problem ID [5257]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary
problems. Page 22
Problem number: 47.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{2}+x y y^{\prime }=-x^{2}} \] With initial conditions \begin {align*} [y \left (1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
dsolve([(x^2+y(x)^2)+x*y(x)*diff(y(x),x)= 0,y(1) = -1],y(x), singsol=all)
\[ y = -\frac {\sqrt {-2 x^{4}+6}}{2 x} \]
✓ Solution by Mathematica
Time used: 0.202 (sec). Leaf size: 26
DSolve[{(x^2+y[x]^2)+x*y[x]*y'[x]==0,{y[1]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sqrt {3-x^4}}{\sqrt {2} x} \]