4.42.13 $y^{″}(x{)}^2=a+b{y}^{\prime }(x{)}^2$

ODE
$$y^{″}(x{)}^2=a+b{y}^{\prime }(x{)}^2$$ ODE Classification

[[_2nd_order, _missing_x]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.155287 (sec), leaf count = 101

$$\{\{y(x)\to c_2-\frac{e^{-\sqrt{b}(c_1+x)}(ab{e}^{2\sqrt{b}x}+e^{2\sqrt{b}{c}_1})}{2b^{3/2}}\},\{y(x)\to \frac{e^{-\sqrt{b}(c_1+x)}(ab+e^{2\sqrt{b}(c_1+x)})}{2b^{3/2}}+c_2\}\}$$

Maple ✓
cpu = 0.293 (sec), leaf count = 92

$$\{y\left(x\right)=-\frac{x}{b}\sqrt{-ab}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\frac{x}{b}\sqrt{-ab}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\sqrt{b}x}+\frac{a}{4b^2\mathit{\_}\mathit{C}\mathit{2}}{\mathrm{e}}^{-\sqrt{b}x},y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}+\frac{a}{4b^2\mathit{\_}\mathit{C}\mathit{2}}{\mathrm{e}}^{\sqrt{b}x}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\sqrt{b}x}\}$$ 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) + E^(2*Sqrt[b]*C[1]))/(2*b^(3/2)*E^(Sqrt[b]*(x +
 C[1]))) + C[2]}, {y[x] -> (a*b + E^(2*Sqrt[b]*(x + C[1])))/(2*b^(3/2)*E^(Sqrt[b
]*(x + C[1]))) + C[2]}}

Maple raw input

dsolve(diff(diff(y(x),x),x)^2 = a+b*diff(y(x),x)^2, y(x),'implicit')

Maple raw output

y(x) = -1/b*(-a*b)^(1/2)*x+_C1, y(x) = 1/b*(-a*b)^(1/2)*x+_C1, y(x) = _C1+_C2*ex
p(b^(1/2)*x)+1/4*a/b^2/_C2*exp(-b^(1/2)*x), y(x) = _C1+1/4*a/b^2/_C2*exp(b^(1/2)
*x)+_C2*exp(-b^(1/2)*x)