##### 4.17.13 $$y'(x)^2-y(x) y'(x)+e^x=0$$

ODE
$y'(x)^2-y(x) y'(x)+e^x=0$ ODE Classiﬁcation

[[_1st_order, _with_linear_symmetries]]

Book solution method
No Missing Variables ODE, Solve for $$y$$

Mathematica
cpu = 0.348365 (sec), leaf count = 137

$\left \{\left \{y(x)\to -\frac {2 i e^{x/2}}{\sqrt {-1+\tanh ^2\left (\frac {x-c_1}{2}\right )}}\right \},\left \{y(x)\to \frac {2 i e^{x/2}}{\sqrt {-1+\tanh ^2\left (\frac {x-c_1}{2}\right )}}\right \},\left \{y(x)\to -\frac {2 i e^{x/2}}{\sqrt {-1+\tanh ^2\left (\frac {-x+c_1}{2}\right )}}\right \},\left \{y(x)\to \frac {2 i e^{x/2}}{\sqrt {-1+\tanh ^2\left (\frac {-x+c_1}{2}\right )}}\right \}\right \}$

Maple
cpu = 2.949 (sec), leaf count = 30

$\left [y \left (x \right ) = -2 \,{\mathrm e}^{\frac {x}{2}}, y \left (x \right ) = 2 \,{\mathrm e}^{\frac {x}{2}}, y \left (x \right ) = \frac {1}{\textit {\_C1}}+\textit {\_C1} \,{\mathrm e}^{x}\right ]$ Mathematica raw input

DSolve[E^x - y[x]*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> ((-2*I)*E^(x/2))/Sqrt[-1 + Tanh[(x - C[1])/2]^2]}, {y[x] -> ((2*I)*E^(
x/2))/Sqrt[-1 + Tanh[(x - C[1])/2]^2]}, {y[x] -> ((-2*I)*E^(x/2))/Sqrt[-1 + Tanh
[(-x + C[1])/2]^2]}, {y[x] -> ((2*I)*E^(x/2))/Sqrt[-1 + Tanh[(-x + C[1])/2]^2]}}

Maple raw input

dsolve(diff(y(x),x)^2-y(x)*diff(y(x),x)+exp(x) = 0, y(x))

Maple raw output

[y(x) = -2*exp(1/2*x), y(x) = 2*exp(1/2*x), y(x) = 1/_C1+_C1*exp(x)]