Differentiate the given solution:
Substitute and
into the ODE:
and it's easy to see the left side indeed reduces to 0.
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The general equation of line with the slope "m" and passing points (a,b) is :
y - b = m (x -a)
In the given question:
Slope m = -2, passing points (a,b) = (4,-4)
Substitute the value of a = 4, b = -4 in the general equation of line
The equation with the slope -2 and passing points (4,-4) is 2x + y = 4
Answer : 2x + y = 4