Internal problem ID [7873]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 293.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {x \left (y^{2}-3 x \right ) y^{\prime }+2 y^{3}-5 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.1 (sec). Leaf size: 36
dsolve(x*(y(x)^2-3*x)*diff(y(x),x)+2*y(x)^3-5*x*y(x)=0,y(x), singsol=all)
\[ \ln \relax (x )-c_{1}+\frac {6 \ln \left (\frac {y \relax (x )}{\sqrt {x}}\right )}{13}-\frac {2 \ln \left (-\frac {-5 y \relax (x )^{2}+13 x}{x}\right )}{65} = 0 \]
✓ Solution by Mathematica
Time used: 2.359 (sec). Leaf size: 661
DSolve[x*(y[x]^2-3*x)*y'[x]+2*y[x]^3-5*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,1\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,2\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,3\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,4\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,5\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,6\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,7\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,8\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,9\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,10\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,11\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,12\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,13\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,14\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^{15}-\frac {25 \text {$\#$1}^2 e^{\frac {65 c_1}{2}}}{x^{26}}+\frac {65 e^{\frac {65 c_1}{2}}}{x^{25}}\&,15\right ] \\ \end{align*}