Internal problem ID [994]
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: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x y^{3} y^{\prime }-y^{4}-x^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 58
dsolve(x*y(x)^3*diff(y(x),x)=y(x)^4+x^4,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (4 \ln \relax (x )+c_{1}\right )^{\frac {1}{4}} x \\ y \relax (x ) = -\left (4 \ln \relax (x )+c_{1}\right )^{\frac {1}{4}} x \\ y \relax (x ) = -i \left (4 \ln \relax (x )+c_{1}\right )^{\frac {1}{4}} x \\ y \relax (x ) = i \left (4 \ln \relax (x )+c_{1}\right )^{\frac {1}{4}} x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.195 (sec). Leaf size: 76
DSolve[x*y[x]^3*y'[x]==y[x]^4+x^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt [4]{4 \log (x)+c_1} \\ y(x)\to -i x \sqrt [4]{4 \log (x)+c_1} \\ y(x)\to i x \sqrt [4]{4 \log (x)+c_1} \\ y(x)\to x \sqrt [4]{4 \log (x)+c_1} \\ \end{align*}