Question

dy/dx= -4xy²; y(0)=1,Solve the given differential equation.Also find particular solution where intial conditions are given.

Answer 1

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@karangrover12.

Answer 2

Answer:

2x²y-y+1=0

Step-by-step explanation:

dy/dx=-4xy² is the given differential equation. We have to get a solution for that.

Now, using separation of the variable we have,

dy/y²=-4x dx

Now, integrating both sides, we get,

∫dy/y²=-4∫x dx+c (Where c is an integration constant}

⇒-1/y =-2x²+c .... this is the general solution.

Now, given y(0)=1 i.e. at x=0, y=1.

Hence, putting the values in the general solution, we get.

c =-1.  

Therefore, the particular solution is  

-1/y=-2x²-1,

⇒ 2x²y+y-1=0 . (Answer)