60.1.59 problem 59

Internal problem ID [10073]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 59
Date solved : Monday, January 27, 2025 at 06:21:53 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-a \sqrt {1+y^{2}}-b&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(x),x) - a*sqrt(y(x)^2+1) - b=0,y(x), singsol=all)
 

\[ x -\int _{}^{y}\frac {1}{a \sqrt {\textit {\_a}^{2}+1}+b}d \textit {\_a} +c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.491 (sec). Leaf size: 78

DSolve[D[y[x],x] - a*Sqrt[y[x]^2+1] - b==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\sqrt {K[1]^2+1} a+b}dK[1]\&\right ][x+c_1] \\ y(x)\to -\frac {\sqrt {b^2-a^2}}{a} \\ y(x)\to \frac {\sqrt {b^2-a^2}}{a} \\ \end{align*}