Internal problem ID [2073]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 43.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {y^{\prime } x -2 y-2 y^{3} x^{4}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 18
dsolve([x*diff(y(x),x)+(-2*y(x)-2*x^4*y(x)^3)=0,y(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 x^{2}}{\sqrt {-2 x^{8}+6}} \]
✓ Solution by Mathematica
Time used: 0.225 (sec). Leaf size: 25
DSolve[{x*y'[x]+(-2*y[x]-2*x^4*y[x]^3)==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt {2} x^2}{\sqrt {3-x^8}} \]