Internal problem ID [987]
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: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x +y-x^{4} y^{4}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (1) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 35
dsolve([x*diff(y(x),x)+y(x)=x^4*y(x)^4,y(1) = 1/2],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-\left (3 x -11\right )^{2}\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{6 x^{2}-22 x} \]
✓ Solution by Mathematica
Time used: 0.418 (sec). Leaf size: 18
DSolve[{x*y'[x]+y[x]==x^4*y[x]^4,y[1]==1/2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\sqrt [3]{(11-3 x) x^3}} \\ \end{align*}