Internal problem ID [4035]
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]
\[ \boxed {{y^{\prime }}^{2}+2 \left (1-x \right ) y^{\prime }+2 y=2 x} \]
✓ Solution by Maple
Time used: 0.032 (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)
\[ y \left (x \right ) = \left (\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{-x}\right )+x +1\right ) x -\frac {{\left (\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{-x}\right )+x \right )}^{2}}{2}-\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{-x}\right )-x \]
✓ Solution by Mathematica
Time used: 1.796 (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 [2 \text {arctanh}\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 )-\sqrt {x^2-2 y(x)+1}+x=c_1,y(x)\right ] \text {Solve}\left [2 \text {arctanh}\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 )+\sqrt {x^2-2 y(x)+1}+x=c_1,y(x)\right ] \end{align*}