18.30 problem 508

Internal problem ID [3252]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 18
Problem number: 508.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class D], _rational, _Bernoulli]

Solve \begin {gather*} \boxed {y y^{\prime } x +x^{4}-y^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 30

dsolve(x*y(x)*diff(y(x),x)+x^4-y(x)^2 = 0,y(x), singsol=all)
 

\begin{align*} y \relax (x ) = \sqrt {-x^{2}+c_{1}}\, x \\ y \relax (x ) = -\sqrt {-x^{2}+c_{1}}\, x \\ \end{align*}

Solution by Mathematica

Time used: 0.365 (sec). Leaf size: 43

DSolve[x y[x] y'[x]+x^4-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {-x^4+c_1 x^2} \\ y(x)\to \sqrt {-x^4+c_1 x^2} \\ \end{align*}