Internal problem ID [3516]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 27
Problem number: 784.
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}+y^{\prime } x +x -y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.068 (sec). Leaf size: 39
dsolve(diff(y(x),x)^2+x*diff(y(x),x)+x-y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \left (\LambertW \left (\frac {c_{1} {\mathrm e}^{\frac {x}{2}-1}}{2}\right )-\frac {x}{2}+2\right ) x +\left (\LambertW \left (\frac {c_{1} {\mathrm e}^{\frac {x}{2}-1}}{2}\right )-\frac {x}{2}+1\right )^{2} \]
✓ Solution by Mathematica
Time used: 2.463 (sec). Leaf size: 177
DSolve[(y'[x])^2+x y'[x]+x -y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [-\sqrt {x^2+4 y(x)-4 x}+2 \log \left (\sqrt {x^2+4 y(x)-4 x}-x+2\right )-2 \log \left (-x \sqrt {x^2+4 y(x)-4 x}+x^2+4 y(x)-2 x-4\right )+x=c_1,y(x)\right ] \\ \text {Solve}\left [\sqrt {x^2+4 y(x)-4 x}-4 \tanh ^{-1}\left (\frac {(x-5) \sqrt {x^2+4 y(x)-4 x}-x^2-4 y(x)+7 x-6}{(x-3) \sqrt {x^2+4 y(x)-4 x}-x^2-4 y(x)+5 x-2}\right )+x=c_1,y(x)\right ] \\ \end{align*}