Question

In: Math

Consider the following differential equation: (t^2)y'-y=(y^2), where y'=dy/dt. (a) find y(t) if y(1)=1/2 (b)find limt->infinityy(t)

Consider the following differential equation:

(t^2)y'-y=(y^2), where y'=dy/dt.

(a) find y(t) if y(1)=1/2

(b)find lim_t->infinityy(t)

Expert Solution

Solution-

Find the solution for the DE given,

use variable separation,

integrate both sides,

Therefore y(t) is

Here k is constant.

(a)

Find the value for k,

y(t) is,

(b)

so,

for x-i>nfinite y(t)->-1

Value for the limit is -1.

milcah answered 1 year ago

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