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 = 0.279077 (sec), leaf count = 22
\[\left \{\left \{y(x)\to c_2-\frac {\log (\cos (a b (x+c_1)))}{b^2}\right \}\right \}\]
Maple ✓
cpu = 0.286 (sec), leaf count = 31
\[\left [y \left (x \right ) = -\frac {\ln \left (\frac {b \left (\textit {\_C1} \sin \left (a b x \right )-\textit {\_C2} \cos \left (a b x \right )\right )}{a}\right )}{b^{2}}\right ]\] 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))
Maple raw output
[y(x) = -ln(b*(_C1*sin(a*b*x)-_C2*cos(a*b*x))/a)/b^2]