Internal problem ID [10306]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 58.
Independent variable absent. Page 135
Problem number: Ex 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y y^{\prime \prime }+2 y^{\prime }-\left (y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(y(x)*diff(y(x),x$2)+2*diff(y(x),x)-diff(y(x),x)^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \frac {{\mathrm e}^{c_{2} c_{1}} {\mathrm e}^{x c_{1}}-2}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 21
DSolve[y[x]*y''[x]+2*y'[x]-y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-2+e^{c_1 (x+c_2)}}{c_1} \\ \end{align*}