a.Express y in terms of x given that dy/dx = (y + 2)(2x + 1) given...

a.Express y in terms of x given that dy/dx = (y + 2)(2x + 1) given that y = 2 at x = 0.
b. Solve (x^2 + 1)dy/dx + 3xy = 6x.
c) Obtain a general solution of dy/dx + y/x = sin x.

Expert Solution

milcah answered 2 years ago

dy/dx+(y/2x)=(x/(y^3))

Let Q1=y(2) Q2 =y(3) where y=y(x) solves y'+2xy=2x^3 y(0)=1 dy/dx= (2x-y)/(x+4y) y(1)=1 y'+ycotx=y^3sin^3x y(pi/2)=1 (y^2-2x)dx+2xy dy=0 ...

Let Q1=y(2) Q2 =y(3) where y=y(x) solves y'+2xy=2x^3 y(0)=1 dy/dx= (2x-y)/(x+4y) y(1)=1 y'+ycotx=y^3sin^3x y(pi/2)=1 (y^2-2x)dx+2xy dy=0 y(1)=1 2x^2y;+4xy=3sinx y(2pi)=0 y"+2y^-1 (y')^2=y'

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