ODE
\[ -(a-2 b x) y'(x)-b y(x)+y(x) y'(x)^2=0 \] ODE Classification
[[_homogeneous, `class C`], _rational, _dAlembert]
Book solution method
Change of variable
Mathematica ✓
cpu = 0.784562 (sec), leaf count = 163
\[\left \{\left \{y(x)\to -\sqrt {e^{2 c_1}-\frac {\sqrt {b e^{2 c_1} (a-2 b x)^2}}{b}}\right \},\left \{y(x)\to \sqrt {e^{2 c_1}-\frac {\sqrt {b e^{2 c_1} (a-2 b x)^2}}{b}}\right \},\left \{y(x)\to -\sqrt {\frac {\sqrt {b e^{2 c_1} (a-2 b x)^2}}{b}+e^{2 c_1}}\right \},\left \{y(x)\to \sqrt {\frac {\sqrt {b e^{2 c_1} (a-2 b x)^2}}{b}+e^{2 c_1}}\right \}\right \}\]
Maple ✓
cpu = 7.571 (sec), leaf count = 197
\[\left [y \left (x \right ) = -\frac {-2 b x +a}{2 \sqrt {-b}}, y \left (x \right ) = \frac {-2 b x +a}{2 \sqrt {-b}}, y \left (x \right ) = \sqrt {\frac {\textit {\_C1} b +\sqrt {4 \textit {\_C1} \,b^{3} x^{2}-4 \textit {\_C1} a \,b^{2} x +\textit {\_C1} \,a^{2} b}}{b}}, y \left (x \right ) = \sqrt {\frac {\textit {\_C1} b -\sqrt {4 \textit {\_C1} \,b^{3} x^{2}-4 \textit {\_C1} a \,b^{2} x +\textit {\_C1} \,a^{2} b}}{b}}, y \left (x \right ) = -\sqrt {\frac {\textit {\_C1} b +\sqrt {4 \textit {\_C1} \,b^{3} x^{2}-4 \textit {\_C1} a \,b^{2} x +\textit {\_C1} \,a^{2} b}}{b}}, y \left (x \right ) = -\sqrt {\frac {\textit {\_C1} b -\sqrt {4 \textit {\_C1} \,b^{3} x^{2}-4 \textit {\_C1} a \,b^{2} x +\textit {\_C1} \,a^{2} b}}{b}}\right ]\] Mathematica raw input
DSolve[-(b*y[x]) - (a - 2*b*x)*y'[x] + y[x]*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[E^(2*C[1]) - Sqrt[b*E^(2*C[1])*(a - 2*b*x)^2]/b]}, {y[x] -> Sqrt[E^(2*C[1]) - Sqrt[b*E^(2*C[1])*(a - 2*b*x)^2]/b]}, {y[x] -> -Sqrt[E^(2*C[1]) + Sqrt[b*E^(2*C[1])*(a - 2*b*x)^2]/b]}, {y[x] -> Sqrt[E^(2*C[1]) + Sqrt[b*E^(2*C[1])*(a - 2*b*x)^2]/b]}}
Maple raw input
dsolve(y(x)*diff(y(x),x)^2-(-2*b*x+a)*diff(y(x),x)-b*y(x) = 0, y(x))
Maple raw output
[y(x) = -1/2/(-b)^(1/2)*(-2*b*x+a), y(x) = 1/2/(-b)^(1/2)*(-2*b*x+a), y(x) = ((_C1*b+(4*_C1*b^3*x^2-4*_C1*a*b^2*x+_C1*a^2*b)^(1/2))/b)^(1/2), y(x) = ((_C1*b-(4*_C1*b^3*x^2-4*_C1*a*b^2*x+_C1*a^2*b)^(1/2))/b)^(1/2), y(x) = -((_C1*b+(4*_C1*b^3*x^2-4*_C1*a*b^2*x+_C1*a^2*b)^(1/2))/b)^(1/2), y(x) = -((_C1*b-(4*_C1*b^3*x^2-4*_C1*a*b^2*x+_C1*a^2*b)^(1/2))/b)^(1/2)]