Doubt from differential equations

#1


Q8

#2

Pls check...

#3

-rsin(theta)d(theta) should be there...typo...pls consider

#4

Some error in typo...so pls ignore the post...i am uploading correct answer pls...

#5

Let x=r,y=\cos \theta

you can rewrite as -xdy+(x^3-2x^2y+y) dx =0

or \dfrac{dy}{dx}+ y(2x - \dfrac{1}{x})=x^2 which is a linear form.

The soln will be ye^{x^2}=\dfrac{x}{2} e^{x^2} (x^2-1)

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#6

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#7

@Hari_Shankar sir, @Tanmay_1 sir can you plz check the approach I did.

#8

Great...excellent...

#9

Excellent..