Internal problem ID [3561]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 830.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-{\mathrm e}^{4 x -2 y} \left (y^{\prime }-1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 2.188 (sec). Leaf size: 259
dsolve(diff(y(x),x)^2 = exp(4*x-2*y(x))*(diff(y(x),x)-1),y(x), singsol=all)
\begin{align*} x -\frac {\sqrt {-\left (4 \,{\mathrm e}^{-4 x +2 y \relax (x )}-1\right ) {\mathrm e}^{-4 y \relax (x )+8 x}}\, {\mathrm e}^{-4 x +2 y \relax (x )} \arctanh \left (\frac {1}{\sqrt {-4 \,{\mathrm e}^{-4 x +2 y \relax (x )}+1}}\right )}{2 \sqrt {-4 \,{\mathrm e}^{-4 x +2 y \relax (x )}+1}}-\frac {\ln \left (2 \,{\mathrm e}^{y \relax (x )-2 x}-1\right )}{4}+\frac {\ln \left ({\mathrm e}^{y \relax (x )-2 x}\right )}{2}-\frac {\ln \left (2 \,{\mathrm e}^{y \relax (x )-2 x}+1\right )}{4}+\frac {\ln \left (4 \,{\mathrm e}^{-4 x +2 y \relax (x )}-1\right )}{4}-c_{1} = 0 \\ x -\frac {\ln \left (2 \,{\mathrm e}^{y \relax (x )-2 x}-1\right )}{4}+\frac {\ln \left ({\mathrm e}^{y \relax (x )-2 x}\right )}{2}-\frac {\ln \left (2 \,{\mathrm e}^{y \relax (x )-2 x}+1\right )}{4}+\frac {\ln \left (4 \,{\mathrm e}^{-4 x +2 y \relax (x )}-1\right )}{4}+\frac {\sqrt {-\left (4 \,{\mathrm e}^{-4 x +2 y \relax (x )}-1\right ) {\mathrm e}^{-4 y \relax (x )+8 x}}\, {\mathrm e}^{-4 x +2 y \relax (x )} \arctanh \left (\frac {1}{\sqrt {-4 \,{\mathrm e}^{-4 x +2 y \relax (x )}+1}}\right )}{2 \sqrt {-4 \,{\mathrm e}^{-4 x +2 y \relax (x )}+1}}-c_{1} = 0 \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y'[x])^2==Exp[4 x -2 y[x]] (y'[x]-1),y[x],x,IncludeSingularSolutions -> True]
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