Internal problem ID [8469]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 889.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(y)]]]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {\left (-8-8 y^{3}+24 y^{\frac {3}{2}} {\mathrm e}^{x}-18 \,{\mathrm e}^{2 x}-8 y^{\frac {9}{2}}+36 y^{3} {\mathrm e}^{x}-54 \,{\mathrm e}^{2 x} y^{\frac {3}{2}}+27 \,{\mathrm e}^{3 x}\right ) {\mathrm e}^{x}}{8 \sqrt {y}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.258 (sec). Leaf size: 47
dsolve(diff(y(x),x) = -1/8*(-8-8*y(x)^3+24*y(x)^(3/2)*exp(x)-18*exp(x)^2-8*y(x)^(9/2)+36*y(x)^3*exp(x)-54*y(x)^(3/2)*exp(x)^2+27*exp(x)^3)*exp(x)/y(x)^(1/2),y(x), singsol=all)
\[ {\mathrm e}^{x}-\frac {2 \ln \left (y \relax (x )^{\frac {3}{2}}-\frac {3 \,{\mathrm e}^{x}}{2}+1\right )}{3}+\frac {2}{3 \left (y \relax (x )^{\frac {3}{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right )}+\frac {2 \ln \left (y \relax (x )^{\frac {3}{2}}-\frac {3 \,{\mathrm e}^{x}}{2}\right )}{3}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 1.136 (sec). Leaf size: 68
DSolve[y'[x] == -1/8*(E^x*(-8 - 18*E^(2*x) + 27*E^(3*x) + 24*E^x*y[x]^(3/2) - 54*E^(2*x)*y[x]^(3/2) - 8*y[x]^3 + 36*E^x*y[x]^3 - 8*y[x]^(9/2)))/Sqrt[y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2}{3} \log \left (y(x)^{3/2}-\frac {3 e^x}{2}\right )+e^x=\frac {4}{9 e^x-6 y(x)^{3/2}}+\frac {2}{3} \log \left (y(x)^{3/2}-\frac {3 e^x}{2}+1\right )+c_1,y(x)\right ] \]