Internal problem ID [5336]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 9. Equations of first order and higher degree. Supplemetary problems. Page
65
Problem number: 30.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y-2 y^{\prime }-\sqrt {{y^{\prime }}^{2}+1}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 221
dsolve(y(x)=2*diff(y(x),x)+sqrt(1+diff(y(x),x)^2),y(x), singsol=all)
\begin{align*} x +\frac {\sqrt {\left (y+1\right )^{2}-2 y+2}}{2}-\operatorname {arcsinh}\left (\frac {\sqrt {3}\, y}{3}\right )-\operatorname {arctanh}\left (\frac {6-2 y}{4 \sqrt {\left (y+1\right )^{2}-2 y+2}}\right )-\frac {\sqrt {\left (y-1\right )^{2}+2 y+2}}{2}+\operatorname {arctanh}\left (\frac {6+2 y}{4 \sqrt {\left (y-1\right )^{2}+2 y+2}}\right )-\ln \left (y-1\right )-\ln \left (y+1\right )-c_{1} = 0 x -\frac {\sqrt {\left (y+1\right )^{2}-2 y+2}}{2}+\operatorname {arcsinh}\left (\frac {\sqrt {3}\, y}{3}\right )+\operatorname {arctanh}\left (\frac {6-2 y}{4 \sqrt {\left (y+1\right )^{2}-2 y+2}}\right )+\frac {\sqrt {\left (y-1\right )^{2}+2 y+2}}{2}-\operatorname {arctanh}\left (\frac {6+2 y}{4 \sqrt {\left (y-1\right )^{2}+2 y+2}}\right )-\ln \left (y-1\right )-\ln \left (y+1\right )-c_{1} = 0 \end{align*}
✓ Solution by Mathematica
Time used: 60.301 (sec). Leaf size: 4821
DSolve[y[x]==2*y'[x]+Sqrt[1+y'[x]^2],y[x],x,IncludeSingularSolutions -> True]
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