Internal problem ID [100]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 y x +y^{\prime } x^{2}-5 y^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 164
dsolve(2*x*y(x)+x^2*diff(y(x),x) = 5*y(x)^4,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {7^{\frac {1}{3}} \left (x \left (7 x^{7} c_{1}+15\right )^{2}\right )^{\frac {1}{3}}}{7 x^{7} c_{1}+15} \\ y \relax (x ) = -\frac {7^{\frac {1}{3}} \left (x \left (7 x^{7} c_{1}+15\right )^{2}\right )^{\frac {1}{3}}}{2 \left (7 x^{7} c_{1}+15\right )}-\frac {i \sqrt {3}\, 7^{\frac {1}{3}} \left (x \left (7 x^{7} c_{1}+15\right )^{2}\right )^{\frac {1}{3}}}{2 \left (7 x^{7} c_{1}+15\right )} \\ y \relax (x ) = -\frac {7^{\frac {1}{3}} \left (x \left (7 x^{7} c_{1}+15\right )^{2}\right )^{\frac {1}{3}}}{2 \left (7 x^{7} c_{1}+15\right )}+\frac {i \sqrt {3}\, 7^{\frac {1}{3}} \left (x \left (7 x^{7} c_{1}+15\right )^{2}\right )^{\frac {1}{3}}}{14 x^{7} c_{1}+30} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.462 (sec). Leaf size: 96
DSolve[2*x*y[x]+x^2*y'[x] == 5*y[x]^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [3]{-7} \sqrt [3]{x}}{\sqrt [3]{15+7 c_1 x^7}} \\ y(x)\to \frac {\sqrt [3]{7} \sqrt [3]{x}}{\sqrt [3]{15+7 c_1 x^7}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{7} \sqrt [3]{x}}{\sqrt [3]{15+7 c_1 x^7}} \\ y(x)\to 0 \\ \end{align*}