D solve ordinary differential equations nonlinear second order odes

eqn = Derivative[2][y][x] == 5 x Derivative[1][y][x] + Derivative[1][y][x]^2;sol = DSolve[eqn, y, x]

DSolve[Derivative[2][y][x] == Derivative[1][y][x]^2 + 5*x*Derivative[1][y][x], y, x]

Plot[Evaluate[y[x] /. sol /. {C[1] -> -1 / 2, C[2] -> -1 / 8}], {x, -0.4, 1}]

-Graphics-

eqn /. sol//Simplify

Derivative[2][y][x] == Derivative[1][y][x]^2 + 5*x*Derivative[1][y][x] /. DSolve[Derivative[2][y][x] == Derivative[1][y][x]^2 + 5*x*Derivative[1][y][x], y, x]

DSolve[y''[x] == Exp[3 * y[x]], y[x], x]

DSolve[Derivative[2][y][x] == E^(3*y[x]), y[x], x]

sol = y[x] /. DSolve[y''[x]  == 3 * y[x] * y'[x]  + (3y[x] ^ 2 + 4 * y[x]  + 1), y[x], x][[1]]//Simplify

y[x] /. Derivative[2][y][x] == 1 + 4*y[x] + 3*y[x]^2 + 3*y[x]*Derivative[1][y][x]

DSolve[7 * y[x] * y''[x]  - 11 * y'[x] ^ 2 == 0, y[x], x]

DSolve[-11*Derivative[1][y][x]^2 + 7*y[x]*Derivative[2][y][x] == 0, y[x], x]

eqn = y''[x]  + y[x] * y'[x] ^ 2 - x ^ 2 * y'[x] == 0;

sol = DSolve[eqn, y[x], x]

DSolve[Derivative[1][y][x]^2*y[x] - x^2*Derivative[1][y][x] + Derivative[2][y][x] == 0, y[x], x]