Which of the following differential equations has as the general solution? A. B. C. D.

Open in App

Solution

The equation is given as,

y= c 1 e x + c 2 e −x

Differentiate both sides of above equation with respect to x,

d dx ( y )= d dx ( c 1 e x + c 2 e −x ) y ′ = c 1 e x − c 2 e −x

Again differentiate above equation with respect to x,

d dx ( y ′ )= d dx ( c 1 e x − c 2 e −x ) y ″ = c 1 e x + c 2 e −x d 2 y d x 2 =y d 2 y d x 2 −y=0

Therefore, option B is correct.

Suggest Corrections

Similar questions

y = c_{1} e^{x} + c_{2} e^{- x}

x \frac{d y}{d x} - y = x^{2}

x^{2} d y + y (x + y) d x = 0

\frac{d y}{d x} = y

\frac{d y}{d x} = \frac{1 - x}{y}

Join BYJU'S Learning Program