y=2 x+3 x satisfies which of the following differential equations? 1. d^2 y d x^2 +y=0 2. ( d y d x )^2+ d y d x =0 Select the correct answer using the code given below.

Step-by-step solution

aligned d y d x & =-2 x+3 x and d^2 y d x^2 & =-2 x-3 x aligned aligned & =-(2 x+3 x) & =-y aligned Hence, d^2 y d x^2 +y=0 satisfied Again, ( d y d x )^2+ d y d x =0 d y d x ( d y d x +1 )=0 either d y d x =0 or d y d x =-1 i.e., -2 x+3 x=0 or, -2 x+3 x=-1 or, 2 x=3 x x= 3 2 This is satisfied for x= ⁻¹ ( 3 2 )