Q. 225.0( 1 Vote )

# Find the equation

Given Slope of the equation at any point (x,y) = x + 3y – 1

We can see that it is a linear differential equation.

Comparing it with

P = – 3, Q = x – 1

I.F = e∫Pdx

= e – 3dx

= e – 3x

Solution of the given equation is given by

y × I.F = ∫Q × I.F dx + c

y × e – 3x = ∫ (x – 1) × e – 3xdx + c

y × e – 3x = (x – 1) × e – 3x – ∫(1)e – 3x dx + c

y × e – 3x = (x – 1) × e – 3x + (e – 3x ) + c

……(1)

As the equation passing through origin(0,0)

0 = 0 + + c

c =

Putting the value of c in equation (1)

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