4.37.9 \(y''(x)=a^2+b^2 y'(x)^2\)

ODE
\[ y''(x)=a^2+b^2 y'(x)^2 \] ODE Classification

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

Book solution method
TO DO

Mathematica
cpu = 0.067127 (sec), leaf count = 22

\[\left \{\left \{y(x)\to c_2-\frac {\log \left (\cos \left (a b \left (c_1+x\right )\right )\right )}{b^2}\right \}\right \}\]

Maple
cpu = 0.053 (sec), leaf count = 29

\[ \left \{ -{\it \_C1}\,\sin \left ( abx \right ) +{\it \_C2}\,\cos \left ( abx \right ) +{{\rm e}^{-{b}^{2}y \left ( x \right ) }}a=0 \right \} \] Mathematica raw input

DSolve[y''[x] == a^2 + b^2*y'[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> C[2] - Log[Cos[a*b*(x + C[1])]]/b^2}}

Maple raw input

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

Maple raw output

-_C1*sin(a*b*x)+_C2*cos(a*b*x)+exp(-b^2*y(x))*a = 0