Math, asked by creativeaquarin, 10 months ago

Find the integrating factor of the differential equation x dy/dx-2y=2x^2

Answers

Answered by r5134497
6

The integrating factor is \dfrac{1}{x^2}

Step-by-step explanation:

Since we know that;

  •   \dfrac{dy}{dx} +Py = Q  

then;  

  • I. F. = e^\int^p^d^x

Differential equation:

  • x \dfrac{dy}{dx}-2y=2x^2

\dfrac{dy}{dx}-\dfrac{2y}{x}=2x

P = \dfrac{-2}{x}, Q = 2x

Now, I.F. =  e^\int^p^d^x

               =e^{\int\dfrac{-2}{x}dx}

               = e^{-2logx}

               = e^{log\left(x\right )^-^2}

               = x^-^2

Therefore,  I.F. = \dfrac{1}{x^2}

Answered by isyllus
1

The integrating factor is \dfrac{1}{x^2}

Step-by-step explanation:

Given that,

x\dfrac{dy}{dx}-2y=2x^2

This is linear differential equation, y' + Py = Q

then Integrating factor, IF=e^{\int Pdx}

First we change the differential equation,

x\dfrac{dy}{dx}-2y=2x^2 into

  y ' +py = Q

\dfrac{dy}{dx}-\dfrac{2y}{x}=2x

where, P=-\dfrac{2}{x},Q=2x

Integrating factor, IF=e^{\int -\dfrac{2}{x}dx}

                              IF=e^{\ln x^{-2}}

                              IF=x^{-2}=\dfrac{1}{x^2}

Hence, the integrating factor is \dfrac{1}{x^2}

#Learn more:

Integrating factor

https://brainly.in/question/11263233

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