15.18.28 problem 28

Internal problem ID [3271]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 28
Date solved : Monday, January 27, 2025 at 07:29:57 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} \left (y+1\right ) y^{\prime \prime }&=3 {y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 59

dsolve((y(x)+1)*diff(y(x),x$2)=3*diff(y(x),x)^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -1 \\ y \left (x \right ) &= -\frac {\sqrt {-2 c_{1} x -2 c_{2}}-1}{\sqrt {-2 c_{1} x -2 c_{2}}} \\ y \left (x \right ) &= -\frac {\sqrt {-2 c_{1} x -2 c_{2}}+1}{\sqrt {-2 c_{1} x -2 c_{2}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.505 (sec). Leaf size: 107

DSolve[(y[x]+1)*D[y[x],{x,2}]==3*D[y[x],x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {2 c_1 x+\sqrt {2} \sqrt {-c_1 (x+c_2)}+2 c_2 c_1}{2 c_1 (x+c_2)} \\ y(x)\to \frac {-2 c_1 x+\sqrt {2} \sqrt {-c_1 (x+c_2)}-2 c_2 c_1}{2 c_1 (x+c_2)} \\ y(x)\to -1 \\ y(x)\to \text {Indeterminate} \\ \end{align*}