60.2.320 problem 897

Internal problem ID [10907]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 897
Date solved : Tuesday, January 28, 2025 at 05:30:33 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {\left (-108 x^{{3}/{2}} y+18 x^{{9}/{2}}-108 x^{{3}/{2}}-216 y^{3}+108 x^{3} y^{2}-18 y x^{6}+x^{9}\right ) \sqrt {x}}{-216 y+36 x^{3}-216} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 87

dsolve(diff(y(x),x) = (-108*x^(3/2)*y(x)+18*x^(9/2)-108*x^(3/2)-216*y(x)^3+108*x^3*y(x)^2-18*y(x)*x^6+x^9)*x^(1/2)/(-216*y(x)+36*x^3-216),y(x), singsol=all)
 

\begin{align*} y &= \frac {\sqrt {9 c_{1} -12 x^{{3}/{2}}}\, x^{3}-3 x^{3}+18}{6 \sqrt {9 c_{1} -12 x^{{3}/{2}}}-18} \\ y &= \frac {\sqrt {9 c_{1} -12 x^{{3}/{2}}}\, x^{3}+3 x^{3}-18}{6 \sqrt {9 c_{1} -12 x^{{3}/{2}}}+18} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.076 (sec). Leaf size: 76

DSolve[D[y[x],x] == (Sqrt[x]*(-108*x^(3/2) + 18*x^(9/2) + x^9 - 108*x^(3/2)*y[x] - 18*x^6*y[x] + 108*x^3*y[x]^2 - 216*y[x]^3))/(-216 + 36*x^3 - 216*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^3}{6}-\frac {216}{216+\sqrt {-62208 x^{3/2}+c_1}} \\ y(x)\to \frac {x^3}{6}+\frac {216}{-216+\sqrt {-62208 x^{3/2}+c_1}} \\ y(x)\to \frac {x^3}{6} \\ \end{align*}