If (2+sin x) frac{dy}{dx} + (y+1) cos x = 0 a | vedclass

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

Question

(D) Given the differential equation: $(2+\sin x) \frac{dy}{dx} + (y+1) \cos x = 0$ Rearranging the terms to separate the variables: $\frac{dy}{y+1} =

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(D) Given the differential equation: $(2+\sin x) \frac{dy}{dx} + (y+1) \cos x = 0$ Rearranging the terms to separate the variables: $\frac{dy}{y+1} = -\frac{\cos x}{2+\sin x} dx$ Integrating both sides: $\int \frac{dy}{y+1} = -\int \frac{\cos x}{2+\sin x} dx$ $\ln(y+1) = -\ln(2+\sin x) + C$ $\ln(y+1) + \ln(2+\sin x) = C$ $\ln((y+1)(2+\sin x)) = C$ $(y+1)(2+\sin x) = e^C = K$ Given $y(0) = 1$,substitute $x=0$ and $y=1$: $(1+1)(2+\sin 0) = K \Rightarrow 2(2+0) = K \Rightarrow K = 4$ So,$(y+1)(2+\sin x) = 4$ For $x = \frac{\pi}{2}$: $(y+1)(2+\sin \frac{\pi}{2}) = 4$ $(y+1)(2+1) = 4$ $3(y+1) = 4$ $y+1 = \frac{4}{3}$ $y = \frac{4}{3} - 1 = \frac{1}{3}$

If $(2+\sin x) \frac{dy}{dx} + (y+1) \cos x = 0$ and $y(0) = 1$,then $y\left(\frac{\pi}{2}\right)$ is

Similar Questions

Two concentric coils of $10$ turns each are placed in the same plane. Their radii are $20 \ cm$ and $40 \ cm$ and carry $0.2 \ A$ and $0.3 \ A$ current respectively in opposite directions. The magnetic induction (in $T$) at the centre is

When iron sulfide is heated in air,a sulfur oxide $A$ is formed. When $A$ is dissolved in water,it produces an acid. What is the basicity of this acid?

Write the resonance structures of $CO_3^{2-}$ and $HCO_3^-$.

Which part of the world has a high density of organisms?

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod perpendicular to its length. The acceleration of the centre of mass of the rod is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module