For which values of t0 a1 a2 and a3 does the IVP y cos 2t y

For which values of t_0, a_1, a_2, and a_3, does the IVP y\"\' = cos (2t) y^2 + + (y\")^7/5/sin t + 3(y\')^1/5; y(t_0) = a_1, y\'(t_0) = a_2, y\"(t_0) = a_3, have a solution and have a unique solution, respectively? Justify your answers.

Solution

a2 equal to zero and t0 = k.pi + pi/2 for all k in that case given ivp has unique solution