60.2.305 problem 882

Internal problem ID [10892]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 882
Date solved : Monday, January 27, 2025 at 10:21:33 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]

\begin{align*} y^{\prime }&=-\frac {\left (-108 x^{{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} \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y = \frac {x^{3}}{6}-\frac {1}{3}+\frac {29 \operatorname {RootOf}\left (2 x^{{3}/{2}}-243 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+9 c_{1} \right )}{9} \]

✓ Solution by Mathematica

Time used: 0.212 (sec). Leaf size: 97

DSolve[D[y[x],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]
 

\[ \text {Solve}\left [\int _1^{\frac {\frac {1}{2} \left (2 \sqrt {x}-x^{7/2}\right )+3 \sqrt {x} y(x)}{\sqrt [3]{29} \sqrt [3]{x^{3/2}}}}\frac {1}{K[1]^3-\frac {3 K[1]}{29^{2/3}}+1}dK[1]=\frac {2}{27} 29^{2/3} \sqrt {x} \left (x^{3/2}\right )^{2/3}+c_1,y(x)\right ] \]