ODE
\[ y'(x)^2=a+b y(x)^2 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.0973104 (sec), leaf count = 93
\[\left \{\left \{y(x)\to \frac {e^{-\sqrt {b} \left (c_1+x\right )} \left (e^{2 \sqrt {b} \left (c_1+x\right )}-a b\right )}{2 b}\right \},\left \{y(x)\to \frac {e^{-\sqrt {b} \left (c_1+x\right )} \left (e^{2 \sqrt {b} c_1}-a b e^{2 \sqrt {b} x}\right )}{2 b}\right \}\right \}\]
Maple ✓
cpu = 0.036 (sec), leaf count = 72
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{2}+{\frac {a}{b}}=0,x-{1\ln \left ( \sqrt {b}y \left ( x \right ) +\sqrt {a+b \left ( y \left ( x \right ) \right ) ^{2}} \right ) {\frac {1}{\sqrt {b}}}}-{\it \_C1}=0,x+{1\ln \left ( \sqrt {b}y \left ( x \right ) +\sqrt {a+b \left ( y \left ( x \right ) \right ) ^{2}} \right ) {\frac {1}{\sqrt {b}}}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[y'[x]^2 == a + b*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (-(a*b) + E^(2*Sqrt[b]*(x + C[1])))/(2*b*E^(Sqrt[b]*(x + C[1])))}, {y[x] -> (-(a*b*E^(2*Sqrt[b]*x)) + E^(2*Sqrt[b]*C[1]))/(2*b*E^(Sqrt[b]*(x + C[1])))}}
Maple raw input
dsolve(diff(y(x),x)^2 = a+b*y(x)^2, y(x),'implicit')
Maple raw output
y(x)^2+a/b = 0, x-ln(b^(1/2)*y(x)+(a+b*y(x)^2)^(1/2))/b^(1/2)-_C1 = 0, x+ln(b^(1/2)*y(x)+(a+b*y(x)^2)^(1/2))/b^(1/2)-_C1 = 0