## Rajasthan Board RBSE Class 12 Maths Chapter 12 Differential Equation Ex 12.3

Question 1.

Prove that y^{2} = 4a (x + a) is the solution of:

Solution:

Question 2.

Prove that y = ae^{-2x} + be^{x} is the solution:

Solution:

Question 3.

Prove that y = \(\frac { c-x }{ 1+cx } \) is the solution of (1 + x^{2}) \(\frac { dy }{ dx } \) + (1 + y^{2}) = 0

Solution:

Question 4.

Prove that y = a cos (log x) + b sin (log x) is the solution of

Solution:

y = a cos (log x) + b sin (logx)

Differentiating w.r.t. x,

Question 5.

Prove that xy = log y + c is the solution of

Solution: