40.5.14 problem 30

Internal problem ID [6679]
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
Date solved : Monday, January 27, 2025 at 02:20:51 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.024 (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}{3}\right )+\operatorname {arctanh}\left (\frac {3+y}{2 \sqrt {y^{2}+3}}\right )+\operatorname {arctanh}\left (\frac {-3+y}{2 \sqrt {y^{2}+3}}\right )-\ln \left (y-1\right )-\ln \left (y+1\right )-c_1 &= 0 \\ x +\operatorname {arcsinh}\left (\frac {\sqrt {3}\, y}{3}\right )-\operatorname {arctanh}\left (\frac {3+y}{2 \sqrt {y^{2}+3}}\right )-\operatorname {arctanh}\left (\frac {-3+y}{2 \sqrt {y^{2}+3}}\right )-\ln \left (y-1\right )-\ln \left (y+1\right )-c_1 &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 60.327 (sec). Leaf size: 4821

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

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