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Solution of diffrential equation x\frac{dy}{dx} + y = x^2  is

  • Option 1)

    x^3+3xy= c

  • Option 2)

    x^3-3xy= c

  • Option 3)

    x^3- 3y= c

  • Option 4)

    x^3+3y= c

 

Answers (1)

best_answer

As we have learned

Linear Differential Equation -

Multiply by e^{SPdx}  which is the Integrating factor

- wherein

P is the function of x alone

 

 Given equation can be written as dy/dx + (1/x)y = x 

on comparing it with dy/dx+py=Q , we get P = 1/x

Integrating factor is e^{\int (1/x) dx}= e^{lnx}=x

Multiplying both side by integrating factor i.e x we get 

x\frac{dy}{dx}+ y = x^2 \Rightarrow d/dx (xy) = x^2 \Rightarrow d(xy)= x^2dx

\Rightarrow \int d(xy)- \int x^2dx = C

\Rightarrow xy - x^3/3 = C

\Rightarrow 3xy - x^3= 3C   

can be written  as \Rightarrow x^3- 3xy = C

 

 

 


Option 1)

x^3+3xy= c

Option 2)

x^3-3xy= c

Option 3)

x^3- 3y= c

Option 4)

x^3+3y= c

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gaurav

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