Question

The degree of the differential equation whose general solution is given by y = (c₁ + c₂) cos (x + c₃) – c₄$e^{x + c_{5}}$ where c₁, c₂, c₃, c₄, c₅ are arbitrary constants, is –

• A. 5
• B. 4
• C. 1
• D. 2

Answer 1

Answer: (C)

1

Answer 2

We can write y = A cos (x + B) – Ce^x

where A = c₁ + c₂, B = c₃ and C = c₄$e^{c_{5}}$

$\frac{dy}{dx}$ = – A sin (x + B) – Ce^x

Ž$\frac{d^{2}y}{dx^{2}}$ = – A cos (x + B) – Ce^x

Ž $\frac{d^{2}y}{dx^{2}}$ + y = – 2Ce^x

Ž$\frac{d^{3}y}{dx^{3}}$ + $\frac{dy}{dx}$ = –2 Ce^x = $\frac{d^{2}y}{dx^{2}}$ + y

Ž$\frac{d^{3}y}{dx^{3}}$ – $\frac{d^{2}y}{dx^{2}}$ + $\frac{dy}{dx}$ – y = 0

Which is a differential equation of degree 1.

Hence (3) is the correct answer