Internal problem ID [8525]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 945.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-32 y x -8 x^{3}-16 a \,x^{2}-32 x +64 y^{3}+48 y^{2} x^{2}+96 a x y^{2}+12 y x^{4}+48 y a \,x^{3}+48 y a^{2} x^{2}+x^{6}+6 a \,x^{5}+12 a^{2} x^{4}+8 a^{3} x^{3}}{64 y+16 x^{2}+32 a x +64}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 41
dsolve(diff(y(x),x) = (-32*x*y(x)-8*x^3-16*a*x^2-32*x+64*y(x)^3+48*x^2*y(x)^2+96*a*x*y(x)^2+12*y(x)*x^4+48*y(x)*a*x^3+48*a^2*x^2*y(x)+x^6+6*x^5*a+12*a^2*x^4+8*a^3*x^3)/(64*y(x)+16*x^2+32*a*x+64),y(x), singsol=all)
\[ y \relax (x ) = -\frac {x^{2}}{4}-\frac {a x}{2}+\RootOf \left (-x +\int _{}^{\textit {\_Z}}\frac {2 \textit {\_a} +2}{2 \textit {\_a}^{3}+\textit {\_a} a +a}d \textit {\_a} +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.801 (sec). Leaf size: 213
DSolve[y'[x] == (-32*x - 16*a*x^2 - 8*x^3 + 8*a^3*x^3 + 12*a^2*x^4 + 6*a*x^5 + x^6 - 32*x*y[x] + 48*a^2*x^2*y[x] + 48*a*x^3*y[x] + 12*x^4*y[x] + 96*a*x*y[x]^2 + 48*x^2*y[x]^2 + 64*y[x]^3)/(64 + 32*a*x + 16*x^2 + 64*y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x-4 \text {RootSum}\left [\text {$\#$1}^6+6 \text {$\#$1}^5 a+12 \text {$\#$1}^4 a^2+12 \text {$\#$1}^4 y(x)+8 \text {$\#$1}^3 a^3+48 \text {$\#$1}^3 a y(x)+48 \text {$\#$1}^2 a^2 y(x)+8 \text {$\#$1}^2 a+48 \text {$\#$1}^2 y(x)^2+16 \text {$\#$1} a^2+96 \text {$\#$1} a y(x)^2+32 a y(x)+32 a+64 y(x)^3\&,\frac {\text {$\#$1}^2 \log (x-\text {$\#$1})+2 \text {$\#$1} a \log (x-\text {$\#$1})+4 y(x) \log (x-\text {$\#$1})+4 \log (x-\text {$\#$1})}{3 \text {$\#$1}^4+12 \text {$\#$1}^3 a+12 \text {$\#$1}^2 a^2+24 \text {$\#$1}^2 y(x)+48 \text {$\#$1} a y(x)+8 a+48 y(x)^2}\&\right ]=c_1,y(x)\right ] \]