Internal problem ID [1981]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 9, page 38
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {y \left (1-x^{4} y^{2}\right )+y^{\prime } x=0} \] With initial conditions \begin {align*} [y \left (1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 18
dsolve([y(x)*(1-x^4*y(x)^2)+x*diff(y(x),x)=0,y(1) = -1],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{\sqrt {-x^{2}+2}\, x} \]
✓ Solution by Mathematica
Time used: 0.39 (sec). Leaf size: 21
DSolve[{y[x]*(1-x^4*y[x]^2)+x*y'[x]==0,{y[1]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{\sqrt {-x^2 \left (x^2-2\right )}} \]