Internal problem ID [4097]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 859.
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: 0.63 (sec). Leaf size: 84
DSolve[x (y'[x])^2+y[x] y'[x]-y[x]^4==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*}