Internal problem ID [8310]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 730.
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 (2 y^{\frac {3}{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{\frac {3}{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.312 (sec). Leaf size: 49
dsolve(diff(y(x),x) = 1/4*(2*y(x)^(3/2)-3*exp(x))^3*exp(x)/(2*y(x)^(3/2)-3*exp(x)+2)/y(x)^(1/2),y(x), singsol=all)
\[ {\mathrm e}^{x}-\left (\int _{}^{y \relax (x )^{\frac {3}{2}}-\frac {3 \,{\mathrm e}^{x}}{2}}\left (\frac {2 \textit {\_a}}{3 \left (\textit {\_a}^{3}-\textit {\_a} -1\right )}+\frac {2}{3 \left (\textit {\_a}^{3}-\textit {\_a} -1\right )}\right )d \textit {\_a} \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.218 (sec). Leaf size: 83
DSolve[y'[x] == (E^x*(-3*E^x + 2*y[x]^(3/2))^3)/(4*Sqrt[y[x]]*(2 - 3*E^x + 2*y[x]^(3/2))),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {2}{3} \text {RootSum}\left [\text {$\#$1}^3-\text {$\#$1}-1\&,\frac {\text {$\#$1} \log \left (-\text {$\#$1}+y(x)^{3/2}-\frac {3 e^x}{2}\right )+\log \left (-\text {$\#$1}+y(x)^{3/2}-\frac {3 e^x}{2}\right )}{3 \text {$\#$1}^2-1}\&\right ]+e^x-c_1=0,y(x)\right ] \]