60.2.312 problem 889

Internal problem ID [10899]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 889
Date solved : Tuesday, January 28, 2025 at 05:29:29 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} y^{\prime }&=-\frac {\left (-8-8 y^{3}+24 y^{{3}/{2}} {\mathrm e}^{x}-18 \,{\mathrm e}^{2 x}-8 y^{{9}/{2}}+36 y^{3} {\mathrm e}^{x}-54 y^{{3}/{2}} {\mathrm e}^{2 x}+27 \,{\mathrm e}^{3 x}\right ) {\mathrm e}^{x}}{8 \sqrt {y}} \end{align*}

✓ Solution by Maple

Time used: 0.196 (sec). Leaf size: 92

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)
 

\[ \frac {\left (-6 \,{\mathrm e}^{x}+4 y^{{3}/{2}}\right ) \ln \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}+2\right )+\left (6 \,{\mathrm e}^{x}-4 y^{{3}/{2}}\right ) \ln \left (2 y^{{3}/{2}}-3 \,{\mathrm e}^{x}\right )+\left (6 c_{1} -6 \,{\mathrm e}^{x}\right ) y^{{3}/{2}}-9 \,{\mathrm e}^{x} c_{1} +9 \,{\mathrm e}^{2 x}-4}{-6 y^{{3}/{2}}+9 \,{\mathrm e}^{x}} = 0 \]

✓ Solution by Mathematica

Time used: 1.145 (sec). Leaf size: 68

DSolve[D[y[x],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]
 

\[ \text {Solve}\left [\frac {2}{3} \log \left (y(x)^{3/2}-\frac {3 e^x}{2}\right )+e^x=\frac {4}{9 e^x-6 y(x)^{3/2}}+\frac {2}{3} \log \left (y(x)^{3/2}-\frac {3 e^x}{2}+1\right )+c_1,y(x)\right ] \]