NCERT Miscellaneous Exercise Q2 - Differential Equations
Question: Verify that the given functions are solutions: (i) x y = a e^x + b e^{-x} + x^2 of x y'' + 2 y' - x y + x - 2 = 0 (ii) y = e^x (a cos x + b sin x) of y'' - 2 y' + 2y = 0 (iii) y = x sin 3x of y'' + 9y - 6 cos 3x = 0 (iv) x^2 = 2 y^2 log y of (x^2 + y^2) y' - x y = 0.
Answer: Shown/Verified as required.
Full step-by-step NCERT solution with diagrams on Something by Zero.