Internal problem ID [8476]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 896.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x +1+y^{4}-2 y^{2} x^{2}+x^{4}+y^{6}-3 y^{4} x^{2}+3 x^{4} y^{2}-x^{6}}{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 61
dsolve(diff(y(x),x) = (x+1+y(x)^4-2*x^2*y(x)^2+x^4+y(x)^6-3*x^2*y(x)^4+3*x^4*y(x)^2-x^6)/y(x),y(x), singsol=all)
\[ -\left (\int _{\textit {\_b}}^{y \relax (x )}\frac {\textit {\_a}}{\textit {\_a}^{6}-3 \textit {\_a}^{4} x^{2}+3 \textit {\_a}^{2} x^{4}-x^{6}+\textit {\_a}^{4}-2 \textit {\_a}^{2} x^{2}+x^{4}+1}d \textit {\_a} \right )+x -c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.198 (sec). Leaf size: 106
DSolve[y'[x] == (1 + x + x^4 - x^6 - 2*x^2*y[x]^2 + 3*x^4*y[x]^2 + y[x]^4 - 3*x^2*y[x]^4 + y[x]^6)/y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \text {RootSum}\left [-\text {$\#$1}^3+3 \text {$\#$1}^2 y(x)^2+\text {$\#$1}^2-3 \text {$\#$1} y(x)^4-2 \text {$\#$1} y(x)^2+y(x)^6+y(x)^4+1\&,\frac {\log \left (x^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2-6 \text {$\#$1} y(x)^2-2 \text {$\#$1}+3 y(x)^4+2 y(x)^2}\&\right ]-x=c_1,y(x)\right ] \]