Answer:
=13x+12
Step-by-step explanation:
d<em>y</em>/d<em>x</em> = 4 + √(<em>y</em> - 4<em>x</em> + 6)
Make a substitution of <em>v(x)</em> = <em>y(x)</em> - 4<em>x</em> + 6, so that d<em>v</em>/d<em>x</em> = d<em>y</em>/d<em>x</em> - 4. Then the DE becomes
d<em>v</em>/d<em>x</em> + 4 = 4 + √<em>v</em>
d<em>v</em>/d<em>x</em> = √<em>v</em>
which is separable as
d<em>v</em>/√<em>v</em> = d<em>x</em>
Integrating both sides gives
2√<em>v</em> = <em>x</em> + <em>C</em>
Get the solution back in terms of <em>y</em> :
2√(<em>y</em> - 4<em>x</em> + 6) = <em>x</em> + <em>C</em>
You can go on to solve for <em>y</em> explicitly if you want.
√(<em>y</em> - 4<em>x</em> + 6) = <em>x</em>/2 + <em>C</em>
<em>y</em> - 4<em>x</em> + 6 = (<em>x</em>/2 + <em>C </em>)²
<em>y</em> = 4<em>x</em> - 6 + (<em>x</em>/2 + <em>C </em>)²
Answer:
y=5x+1
Step-by-step explanation:
step 1
Find the slope of the given line
we have
(0,1) and (5,0)
m=(0-1)/(5-0)
m=-1/5
step 2
Find the slope of the perpendicular line to the given line
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
m1*m2=-1
m1=-1/5
substitute
(-1/5)*m2=-1
m2=5
step 3
Find the equation of the line with slope m=5 and y-intercept (0,1)
The equation of the line into slope intercept form is equal to
y=mx+b
we have
m=5
b=1
substitute
y=5x+1
Group like terms
7d-14d+12-3
add them
-7d+9
