Internal problem ID [2076]
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: 46.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {y^{\prime } x +y-y^{6} x^{3}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.781 (sec). Leaf size: 54
dsolve([x*diff(y(x),x)+y(x)=x^3*y(x)^6,y(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-\sqrt {5}-1+i \sqrt {10-2 \sqrt {5}}\right ) 2^{\frac {1}{5}} \left (-x^{2} \left (3 x^{2}-5\right )^{4}\right )^{\frac {1}{5}}}{12 x^{3}-20 x} \]
✓ Solution by Mathematica
Time used: 0.473 (sec). Leaf size: 26
DSolve[{x*y'[x]+y[x]==x^3*y[x]^6,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt [5]{2}}{\sqrt [5]{5 x^3-3 x^5}} \]