Internal problem ID [8534]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 954.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {150 x^{3}+125 \sqrt {x}+125+125 y^{2}-100 x^{3} y-500 y \sqrt {x}+20 x^{6}+200 x^{\frac {7}{2}}+500 x +125 y^{3}-150 x^{3} y^{2}-750 y^{2} \sqrt {x}+60 y x^{6}+600 y x^{\frac {7}{2}}+1500 x y-8 x^{9}-120 x^{\frac {13}{2}}-600 x^{4}-1000 x^{\frac {3}{2}}}{125 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.065 (sec). Leaf size: 53
dsolve(diff(y(x),x) = 1/125*(150*x^3+125*x^(1/2)+125+125*y(x)^2-100*x^3*y(x)-500*y(x)*x^(1/2)+20*x^6+200*x^(7/2)+500*x+125*y(x)^3-150*x^3*y(x)^2-750*y(x)^2*x^(1/2)+60*y(x)*x^6+600*y(x)*x^(7/2)+1500*x*y(x)-8*x^9-120*x^(13/2)-600*x^4-1000*x^(3/2))/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {18 x^{\frac {7}{2}}+145 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+\ln \relax (x )+3 c_{1}\right ) \sqrt {x}-15 \sqrt {x}+90 x}{45 \sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.26 (sec). Leaf size: 115
DSolve[y'[x] == (1 + Sqrt[x] + 4*x - 8*x^(3/2) + (6*x^3)/5 + (8*x^(7/2))/5 - (24*x^4)/5 + (4*x^6)/25 - (24*x^(13/2))/25 - (8*x^9)/125 - 4*Sqrt[x]*y[x] + 12*x*y[x] - (4*x^3*y[x])/5 + (24*x^(7/2)*y[x])/5 + (12*x^6*y[x])/25 + y[x]^2 - 6*Sqrt[x]*y[x]^2 - (6*x^3*y[x]^2)/5 + y[x]^3)/x,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\&,\frac {\log \left (\frac {\frac {-6 x^3-30 \sqrt {x}+5}{5 x}+\frac {3 y(x)}{x}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^3}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\&\right ]=\frac {1}{9} 29^{2/3} \left (\frac {1}{x^3}\right )^{2/3} x^2 \log (x)+c_1,y(x)\right ] \]