60.1.373 problem 374

Internal problem ID [10387]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 374
Date solved : Monday, January 27, 2025 at 07:38:50 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 66

dsolve(diff(y(x),x)^2-2*diff(y(x),x)-y(x)^2 = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.862 (sec). Leaf size: 104

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

\begin{align*} y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {\text {$\#$1}^2+1}+\text {$\#$1} \log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )+1}{\text {$\#$1}}\&\right ][-x+c_1] \\ y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {\text {$\#$1}^2+1}}{\text {$\#$1}}-\log \left (\sqrt {\text {$\#$1}^2+1}-\text {$\#$1}\right )+\frac {1}{\text {$\#$1}}\&\right ][x+c_1] \\ y(x)\to 0 \\ \end{align*}