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Find the general solution of the given differential equation. dy/dx +2y = e3x
Solution:
Given differential equation dy/dx +2y = e3x
It is a linear differential equation in the form of dy/dx +Py = Q
Here, P=2 and Q= e3x
We first find the integrating factor(IF)
IF= e∫p dx = e∫2 dx =e2x
Then we multiply the differential equation with IF to get
y× IF = ∫Q× IF dx + C
y e2x = ∫e3x .e2x .dx + C
y e2x = ∫e5x .dx + C
⇒ e2x(y) =e5x/5 + C
⇒ y = e5x /5e2x + C /e2x
y = e3x/5 + Ce-2x
Find the general solution of the given differential equation. dy/dx +2y = e3x
Summary:
The general solution of the given differential equation. dy/dx +2y = e3x is y = e3x/5 + Ce-2x
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