Internal problem ID [7994]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 415.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {x {y^{\prime }}^{2}+y y^{\prime }-y^{4}=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 99
dsolve(x*diff(y(x),x)^2+y(x)*diff(y(x),x)-y(x)^4 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {1}{2 \sqrt {-x}} \\ y \left (x \right ) = \frac {1}{2 \sqrt {-x}} \\ y \left (x \right ) = 0 \\ y \left (x \right ) = -\frac {\sqrt {-x \left (\tanh \left (-\frac {\ln \left (x \right )}{2}+\frac {c_{1}}{2}\right )^{2}-1\right )}}{2 x \tanh \left (-\frac {\ln \left (x \right )}{2}+\frac {c_{1}}{2}\right )} \\ y \left (x \right ) = \frac {\sqrt {-x \left (\tanh \left (-\frac {\ln \left (x \right )}{2}+\frac {c_{1}}{2}\right )^{2}-1\right )}}{2 x \tanh \left (-\frac {\ln \left (x \right )}{2}+\frac {c_{1}}{2}\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.558 (sec). Leaf size: 84
DSolve[-y[x]^4 + y[x]*y'[x] + x*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 e^{\frac {c_1}{2}}}{-4 x+e^{c_1}} \\ y(x)\to \frac {2 e^{\frac {c_1}{2}}}{-4 x+e^{c_1}} \\ y(x)\to 0 \\ y(x)\to -\frac {i}{2 \sqrt {x}} \\ y(x)\to \frac {i}{2 \sqrt {x}} \\ \end{align*}