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  • How to solve this problem- Which of the following represents a bernoulli's equation ?

Which of the following represents a bernoulli's equation ? 

  • Option 1)

    x\frac{dy}{dx}+ (\sin y) y = (\cos x)\cdot y^2

  • Option 2)

    x\frac{dy}{dx}+ (\sin x) y = (x)\cdot y^2

  • Option 3)

    x\frac{dy}{dx}+ (\sin y) = (\cos x)\cdot y^2

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we have learned

Bernoulli's Equation -

\frac{dy}{dx}+py =Qy^{n}

- wherein

P,Q are the function of x alone.

 

 (A)\rightarrow \frac{dy}{dx} + \frac{\sin y}{x } y = \frac{\cos x}{x} y^2

here  \frac{\sin y}{x } is not a function of x alone  so it is not a bernoualii's equation 

(B)\rightarrow \frac{dy}{dx} + \frac{\sin y}{x } y =y^2 

 it is comparable with bernoulli's equation and it is a bernoulli's equation 

(C)\rightarrow \frac{dy}{dx} + \frac{\sin y}{x } = \frac{\cos x}{x} y^2 

It is again not comparable with bernoulli's 

so it isnot a bernoulli's equation 

 

 

 

 


Option 1)

x\frac{dy}{dx}+ (\sin y) y = (\cos x)\cdot y^2

Option 2)

x\frac{dy}{dx}+ (\sin x) y = (x)\cdot y^2

Option 3)

x\frac{dy}{dx}+ (\sin y) = (\cos x)\cdot y^2

Option 4)

none of these

Posted by

gaurav

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