Internal problem ID [8655]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 319.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\left (7 y^{3} x +y-5 x \right ) y^{\prime }+y^{4}-5 y=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 34
dsolve((7*x*y(x)^3+y(x)-5*x)*diff(y(x),x)+y(x)^4-5*y(x) = 0,y(x), singsol=all)
\[ x +\frac {\frac {y \left (x \right )^{5}}{5}-\frac {5 y \left (x \right )^{2}}{2}-c_{1}}{\left (y \left (x \right )^{3}-5\right )^{2} y \left (x \right )} = 0 \]
✓ Solution by Mathematica
Time used: 49.593 (sec). Leaf size: 342
DSolve[-5*y[x] + y[x]^4 + (-5*x + y[x] + 7*x*y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\&,1\right ] \\ y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\&,2\right ] \\ y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\&,3\right ] \\ y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\&,4\right ] \\ y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\&,5\right ] \\ y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\&,6\right ] \\ y(x)\to \text {Root}\left [10 \text {$\#$1}^7 x+2 \text {$\#$1}^5-100 \text {$\#$1}^4 x-25 \text {$\#$1}^2+250 \text {$\#$1} x-10 c_1\&,7\right ] \\ y(x)\to 0 \\ y(x)\to -\sqrt [3]{-5} \\ y(x)\to \sqrt [3]{5} \\ y(x)\to (-1)^{2/3} \sqrt [3]{5} \\ \end{align*}