60.2.154 problem 730

Internal problem ID [10741]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 730
Date solved : Tuesday, January 28, 2025 at 05:10:13 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} y^{\prime }&=\frac {\left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}\right )^{3} {\mathrm e}^{x}}{4 \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}+2\right ) \sqrt {y}} \end{align*}

✓ Solution by Maple

Time used: 0.248 (sec). Leaf size: 37

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)
 

\[ {\mathrm e}^{x}-\frac {2 \left (\int _{}^{y^{{3}/{2}}-\frac {3 \,{\mathrm e}^{x}}{2}}\frac {\textit {\_a} +1}{\textit {\_a}^{3}-\textit {\_a} -1}d \textit {\_a} \right )}{3}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.235 (sec). Leaf size: 56

DSolve[D[y[x],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]
 

\[ \text {Solve}\left [-\int _1^{y(x)^{3/2}-\frac {3 e^x}{2}}\frac {2 K[1]+2}{3 K[1]^3-3 K[1]-3}dK[1]+e^x-c_1=0,y(x)\right ] \]