#### 4.2062

ODE

ODE Classification

[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

Book solution method
TO DO

Mathematica
cpu = 0.850654 (sec), leaf count = 119

Maple
cpu = 0.441 (sec), leaf count = 173

Mathematica raw input

DSolve[y''[x]^2 == a + b*y[x],y[x],x]

Mathematica raw output

{Solve[(Hypergeometric2F1[1/2, 2/3, 5/3, (-4*(a + b*y[x])^(3/2))/(3*b*C[1])]^2*(
a + b*y[x])^2)/(b^2*C[1]) == (x + C[2])^2, y[x]], Solve[(Hypergeometric2F1[1/2,
2/3, 5/3, (4*(a + b*y[x])^(3/2))/(3*b*C[1])]^2*(a + b*y[x])^2)/(b^2*C[1]) == (x
+ C[2])^2, y[x]]}

Maple raw input

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

Maple raw output

y(x) = -a/b, Intat(b*3^(1/2)/(b*(4*_a*(_a*b+a)^(1/2)*b+4*a*(_a*b+a)^(1/2)-_C1))^
(1/2),_a = y(x))-x-_C2 = 0, Intat(-b*3^(1/2)/(b*(4*_a*(_a*b+a)^(1/2)*b+4*a*(_a*b
+a)^(1/2)-_C1))^(1/2),_a = y(x))-x-_C2 = 0, Intat(-3*b/(-12*b*((_a*b+a)^(3/2)-1/
4*_C1))^(1/2),_a = y(x))-x-_C2 = 0, Intat(3*b/(-12*b*((_a*b+a)^(3/2)-1/4*_C1))^(
1/2),_a = y(x))-x-_C2 = 0