Solve each of the following initial value problems ,y(1) = 2 A differential equation is shown: dy/dx = y(x+2y) / x(2x+y).

Q36 of 462 Page 23

Solve each of the following initial value problems
,y(1) = 2

,y(1) = 2

It is a homogeneous equation

Put y = vx

And

So,

…… (1)

2 + v = (A + B)v –A

Comparing the coefficient of like power of v,

A = – 2

A + B = 1

– 2 + B = 1

B = 3

Using in eq. (1)

– 2 log v + 3log (v – 1) = log x + c

Put the value of v,

Solve each of the following initial value problems

,y(1) = 0

Solve each of the following initial value problems

(xy–y²)dx+x²dy=0,y(1) = 1

Solve each of the following initial value problems

,y(1) = 1