Internal problem ID [6093]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 6. Existence and uniqueness of solutions to systems and nth order equations.
Page 238
Problem number: 1(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y y^{\prime \prime }+4 {y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 158
dsolve(y(x)*diff(y(x),x$2)+4*diff(y(x),x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \left (5 c_{1} x +5 c_{2} \right )^{\frac {1}{5}} \\ y \left (x \right ) &= -\frac {\left (i \sqrt {2}\, \sqrt {5-\sqrt {5}}+\sqrt {5}+1\right ) \left (5 c_{1} x +5 c_{2} \right )^{\frac {1}{5}}}{4} \\ y \left (x \right ) &= \frac {\left (i \sqrt {2}\, \sqrt {5-\sqrt {5}}-\sqrt {5}-1\right ) \left (5 c_{1} x +5 c_{2} \right )^{\frac {1}{5}}}{4} \\ y \left (x \right ) &= -\frac {\left (i \sqrt {2}\, \sqrt {5+\sqrt {5}}-\sqrt {5}+1\right ) \left (5 c_{1} x +5 c_{2} \right )^{\frac {1}{5}}}{4} \\ y \left (x \right ) &= \frac {\left (i \sqrt {2}\, \sqrt {5+\sqrt {5}}+\sqrt {5}-1\right ) \left (5 c_{1} x +5 c_{2} \right )^{\frac {1}{5}}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.178 (sec). Leaf size: 20
DSolve[y[x]*y''[x]+4*(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 \sqrt [5]{5 x-c_1} \]