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)]