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]
\[ \boxed {y-2 y^{\prime }-\sqrt {1+{y^{\prime }}^{2}}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 125
dsolve(y(x)=2*diff(y(x),x)+sqrt(1+diff(y(x),x)^2),y(x), singsol=all)
\begin{align*} x -\operatorname {arcsinh}\left (\frac {\sqrt {3}\, y \left (x \right )}{3}\right )+\operatorname {arctanh}\left (\frac {3+y \left (x \right )}{2 \sqrt {y \left (x \right )^{2}+3}}\right )+\operatorname {arctanh}\left (\frac {-3+y \left (x \right )}{2 \sqrt {y \left (x \right )^{2}+3}}\right )-\ln \left (y \left (x \right )-1\right )-\ln \left (y \left (x \right )+1\right )-c_{1} &= 0 \\ x +\operatorname {arcsinh}\left (\frac {\sqrt {3}\, y \left (x \right )}{3}\right )-\operatorname {arctanh}\left (\frac {3+y \left (x \right )}{2 \sqrt {y \left (x \right )^{2}+3}}\right )-\operatorname {arctanh}\left (\frac {-3+y \left (x \right )}{2 \sqrt {y \left (x \right )^{2}+3}}\right )-\ln \left (y \left (x \right )-1\right )-\ln \left (y \left (x \right )+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]
Too large to display