Internal problem ID [3527]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 27
Problem number: 795.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+2 \left (1-x \right ) y^{\prime }-2 x +2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.171 (sec). Leaf size: 45
dsolve(diff(y(x),x)^2+2*(1-x)*diff(y(x),x)-2*x+2*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \left (\LambertW \left (-{\mathrm e}^{-x} c_{1}\right )+x +1\right ) x -\frac {\left (\LambertW \left (-{\mathrm e}^{-x} c_{1}\right )+x \right )^{2}}{2}-\LambertW \left (-{\mathrm e}^{-x} c_{1}\right )-x \]
✓ Solution by Mathematica
Time used: 1.13 (sec). Leaf size: 171
DSolve[(y'[x])^2+2(1-x)y'[x]-2(x-y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [-\sqrt {x^2-2 y(x)+1}+2 \tanh ^{-1}\left (\frac {(x-2) \sqrt {x^2-2 y(x)+1}-x^2+2 y(x)+2 x-1}{x \sqrt {x^2-2 y(x)+1}-x^2+2 y(x)-1}\right )+x=c_1,y(x)\right ] \\ \text {Solve}\left [\sqrt {x^2-2 y(x)+1}+2 \tanh ^{-1}\left (\frac {x \sqrt {x^2-2 y(x)+1}-x^2+2 y(x)-1}{(x+2) \sqrt {x^2-2 y(x)+1}-x^2+2 y(x)-2 x-1}\right )+x=c_1,y(x)\right ] \\ \end{align*}