62.17.5 problem Ex 5

Internal problem ID [12905]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 28. Summary. Page 59
Problem number : Ex 5
Date solved : Tuesday, January 28, 2025 at 04:41:01 AM
CAS classification : [[_homogeneous, `class C`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.102 (sec). Leaf size: 53

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

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

✓ Solution by Mathematica

Time used: 0.067 (sec). Leaf size: 57

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

\begin{align*} y(x)\to x-c_1 \sqrt {x+1}+1+\frac {c_1{}^2}{4} \\ y(x)\to x+c_1 \sqrt {x+1}+1+\frac {c_1{}^2}{4} \\ y(x)\to 0 \\ \end{align*}