Internal problem ID [4024]
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]
\[ \boxed {{y^{\prime }}^{2}+x y^{\prime }-y=-x} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 36
dsolve(diff(y(x),x)^2+x*diff(y(x),x)+x-y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = x -\frac {x^{2}}{4}+\operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-1+\frac {x}{2}}}{2}\right )^{2}+2 \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-1+\frac {x}{2}}}{2}\right )+1 \]
✓ Solution by Mathematica
Time used: 3.196 (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 [-4 \text {arctanh}\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 )+\sqrt {x^2+4 y(x)-4 x}+x&=c_1,y(x)\right ] \\ \end{align*}