The differential equation whose solution is y | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the equation $y = A\sin x + B\cos x$. Differentiating with respect to $x$ once,we get: $\frac{dy}{dx} = A\cos x - B\sin x$. Differentiating

Vedclass · Accepted Answer

$\frac{d^2y}{dx^2} + y = 0$

Vedclass · Answer

(A) Given the equation $y = A\sin x + B\cos x$. Differentiating with respect to $x$ once,we get: $\frac{dy}{dx} = A\cos x - B\sin x$. Differentiating with respect to $x$ again,we get: $\frac{d^2y}{dx^2} = -A\sin x - B\cos x$. We can rewrite this as: $\frac{d^2y}{dx^2} = -(A\sin x + B\cos x)$. Since $y = A\sin x + B\cos x$,we substitute $y$ into the equation: $\frac{d^2y}{dx^2} = -y$. Rearranging the terms,we get the required differential equation: $\frac{d^2y}{dx^2} + y = 0$.

The differential equation whose solution is $y = A\sin x + B\cos x$ is

Similar Questions

The order of the differential equation of all parabolas whose axis of symmetry is along the $X$-axis is:

The differential equation of all circles having their centres on the line $y=5$ and touching the $X$-axis is ......

If $c$ is a parameter,then the differential equation of the family of curves $x^2=c(y+c)^2$ is

Form the differential equation of the family of hyperbolas having foci on the $x$-axis and centre at the origin.

The differential equation of all the lines in the $xy$-plane is

Vedclass Test Series

Exam Paper Generator

Online Exam Module