Internal problem ID [6306]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{\prime }-\frac {-y x -1}{4 y x^{3}-2 x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.344 (sec). Leaf size: 37
dsolve(diff(y(x),x)=(-x*y(x)-1)/(4*x^3*y(x)-2*x^2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{25} c_{1} -10 \textit {\_Z}^{20} c_{1} +25 \textit {\_Z}^{15} c_{1} -16 x^{5}\right )^{5}-1}{4 x} \]
✓ Solution by Mathematica
Time used: 13.595 (sec). Leaf size: 391
DSolve[y'[x] == (-x*y[x]-1)/(4*x^3*y[x]-2*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [64 \text {$\#$1}^5 c_1{}^5 x^5-80 \text {$\#$1}^4 c_1{}^5 x^4-20 \text {$\#$1}^3 c_1{}^5 x^3+25 \text {$\#$1}^2 c_1{}^5 x^2+10 \text {$\#$1} c_1{}^5 x-x^5+c_1{}^5\&,1\right ] \\ y(x)\to \text {Root}\left [64 \text {$\#$1}^5 c_1{}^5 x^5-80 \text {$\#$1}^4 c_1{}^5 x^4-20 \text {$\#$1}^3 c_1{}^5 x^3+25 \text {$\#$1}^2 c_1{}^5 x^2+10 \text {$\#$1} c_1{}^5 x-x^5+c_1{}^5\&,2\right ] \\ y(x)\to \text {Root}\left [64 \text {$\#$1}^5 c_1{}^5 x^5-80 \text {$\#$1}^4 c_1{}^5 x^4-20 \text {$\#$1}^3 c_1{}^5 x^3+25 \text {$\#$1}^2 c_1{}^5 x^2+10 \text {$\#$1} c_1{}^5 x-x^5+c_1{}^5\&,3\right ] \\ y(x)\to \text {Root}\left [64 \text {$\#$1}^5 c_1{}^5 x^5-80 \text {$\#$1}^4 c_1{}^5 x^4-20 \text {$\#$1}^3 c_1{}^5 x^3+25 \text {$\#$1}^2 c_1{}^5 x^2+10 \text {$\#$1} c_1{}^5 x-x^5+c_1{}^5\&,4\right ] \\ y(x)\to \text {Root}\left [64 \text {$\#$1}^5 c_1{}^5 x^5-80 \text {$\#$1}^4 c_1{}^5 x^4-20 \text {$\#$1}^3 c_1{}^5 x^3+25 \text {$\#$1}^2 c_1{}^5 x^2+10 \text {$\#$1} c_1{}^5 x-x^5+c_1{}^5\&,5\right ] \\ \end{align*}