Internal problem ID [8124]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 544.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {x^{7} y^{2} \left (y^{\prime }\right )^{3}-\left (3 x^{6} y^{3}-1\right ) \left (y^{\prime }\right )^{2}+3 x^{5} y^{4} y^{\prime }-x^{4} y^{5}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.547 (sec). Leaf size: 7864
dsolve(x^7*y(x)^2*diff(y(x),x)^3-(3*x^6*y(x)^3-1)*diff(y(x),x)^2+3*x^5*y(x)^4*diff(y(x),x)-x^4*y(x)^5=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {2^{\frac {2}{3}}}{3 x^{2}} \\ y \relax (x ) = \frac {-\frac {2^{\frac {2}{3}}}{2}-\frac {i \sqrt {3}\, 2^{\frac {2}{3}}}{2}}{3 x^{2}} \\ y \relax (x ) = \frac {-\frac {2^{\frac {2}{3}}}{2}+\frac {i \sqrt {3}\, 2^{\frac {2}{3}}}{2}}{3 x^{2}} \\ y \relax (x ) = 0 \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.123 (sec). Leaf size: 80
DSolve[-(x^4*y[x]^5) + 3*x^5*y[x]^4*y'[x] - (-1 + 3*x^6*y[x]^3)*y'[x]^2 + x^7*y[x]^2*y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{c_1 x^3+c_1{}^{2/3}} \\ y(x)\to 0 \\ y(x)\to \frac {(-2)^{2/3}}{3 x^2} \\ y(x)\to \frac {2^{2/3}}{3 x^2} \\ y(x)\to -\frac {\sqrt [3]{-1} 2^{2/3}}{3 x^2} \\ \end{align*}