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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Find the general solution of the given differential equation. dy/dx + y = e7x
Solution:
The given differential equation is
dy/dx + y = e7x
It is of the linear differential equation form dy/dx + Py = Q
P = 1 and Q = e7x
Let us find the integrating factor(IF)
I= e∫pdx = e∫1. dx = ex
Now multiply the differential equation with IF
y × IF = ∫Q× IF .dx + C
Substituting the values
ex.y = ex(e7x) + C
ex.(y) = e8x /8 + C
So we get
y = e8x /8 ex + c. e-x
y = e7x/8 + c.e-x
Therefore, the general solution is y = e7x/8 + c.e-x.
Find the general solution of the given differential equation. dy/dx + y = e7x
Summary:
The general solution of the given differential equation dy/dx + y = e7x is y = e7x/8 + c.e-x.
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