62.34.4 problem Ex 4

Internal problem ID [12996]
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
Date solved : Tuesday, January 28, 2025 at 04:47:09 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y y^{\prime \prime }+2 y^{\prime }-{y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.113 (sec). Leaf size: 20

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 &= 0 \\ y &= \frac {{\mathrm e}^{\left (x +c_{2} \right ) c_{1}}-2}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.529 (sec). Leaf size: 26

DSolve[y[x]*D[y[x],{x,2}]+2*D[y[x],x]-D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {-2+e^{c_1 (x+c_2)}}{c_1} \\ y(x)\to \text {Indeterminate} \\ \end{align*}