62.13.5 problem Ex 5

Internal problem ID [12880]
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 24. Equations solvable for \(p\). Page 49
Problem number : Ex 5
Date solved : Tuesday, January 28, 2025 at 04:31:39 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.076 (sec). Leaf size: 17

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

\begin{align*} y &= \operatorname {arcsinh}\left (x \right )+c_{1} \\ y &= -\operatorname {arcsinh}\left (x \right )+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 21

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

\begin{align*} y(x)\to -\text {arcsinh}(x)+c_1 \\ y(x)\to \text {arcsinh}(x)+c_1 \\ \end{align*}