Set2 22 Problem 1 Set2 22 Problem 1 Problem List Next Previo

Set2 2.2: Problem 1

Set2 2.2: Problem 1 Problem List Next Previous (1 point) Find an equation of the curve that satisfies and whose y-intercept is 2. y(x) dy 112y.x dx

Solution:

given equation: dy/dx=112yx^15

dy/y=112x^15 *dx

applying integral on both sides

In(dy/y)=In(112x^15*dx)

as we know In(dy/y)=log y+c and In(x^n)=x^n+1/n+1 +C

we get -> log y +c1=112*x^16/16+c2

log y=7.x^16 +K where (K=c2-c1) considering it as some constant.

applying exponential on both sides we get

y= e^(7.x^16+K)

given y(0)=2-> substituting it in above equation

2=e^(7.0^16+K)

2=e^K->k=log(2)

thus we get equation of the curve as

y(x)=e^[(7.x^16)+log(2)]

y(x)=e^(7.x^16) * e^log(2)

y(x)=2e^(7.x^16)

Solution: y(x)=2.e^(7.x^16)