Internal problem ID [8462]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 882.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]], _Abel]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {\left (-108 x^{\frac {3}{2}}-216-216 y^{2}+72 x^{3} y-6 x^{6}-216 y^{3}+108 x^{3} y^{2}-18 y x^{6}+x^{9}\right ) \sqrt {x}}{216}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 41
dsolve(diff(y(x),x) = -1/216*(-108*x^(3/2)-216-216*y(x)^2+72*x^3*y(x)-6*x^6-216*y(x)^3+108*x^3*y(x)^2-18*y(x)*x^6+x^9)*x^(1/2),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3}}{6}-\frac {1}{3}+\frac {29 \RootOf \left (2 x^{\frac {3}{2}}-243 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+9 c_{1}\right )}{9} \]
✓ Solution by Mathematica
Time used: 0.187 (sec). Leaf size: 119
DSolve[y'[x] == -1/216*(Sqrt[x]*(-216 - 108*x^(3/2) - 6*x^6 + x^9 + 72*x^3*y[x] - 18*x^6*y[x] - 216*y[x]^2 + 108*x^3*y[x]^2 - 216*y[x]^3)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\&,\frac {\log \left (\frac {\frac {1}{2} \left (2 \sqrt {x}-x^{7/2}\right )+3 \sqrt {x} y(x)}{\sqrt [3]{29} \sqrt [3]{x^{3/2}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\&\right ]=\frac {2}{27} 29^{2/3} \sqrt {x} \left (x^{3/2}\right )^{2/3}+c_1,y(x)\right ] \]