Internal problem ID [2710]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 77.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 x^{3}-y^{4}+y^{3} y^{\prime } x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 73
dsolve((2*x^3-y(x)^4)+(x*y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (x^{4} c_{1}+8 x^{3}\right )^{\frac {1}{4}} \\ y \relax (x ) = -\left (x^{4} c_{1}+8 x^{3}\right )^{\frac {1}{4}} \\ y \relax (x ) = -i \left (x^{4} c_{1}+8 x^{3}\right )^{\frac {1}{4}} \\ y \relax (x ) = i \left (x^{4} c_{1}+8 x^{3}\right )^{\frac {1}{4}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.239 (sec). Leaf size: 88
DSolve[(2*x^3-y[x]^4)+(x*y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x^{3/4} \sqrt [4]{8+c_1 x} \\ y(x)\to -i x^{3/4} \sqrt [4]{8+c_1 x} \\ y(x)\to i x^{3/4} \sqrt [4]{8+c_1 x} \\ y(x)\to x^{3/4} \sqrt [4]{8+c_1 x} \\ \end{align*}