Answer:
√109
Step-by-step explanation:
3^2 + 10^2 = c^2
9 + 100 = 109^2
For an eqtuaion wih slope m and goes through point (x1,y1)
equation is
y-y1=m(x-x1)
so
point (-1,6)
slope=-3
y-6=-3(x-(-1))
y-6=-3(x+1)
2nd one
The differential equation

has characteristic equation
<em>r</em> ⁴ - <em>n </em>² <em>r</em> ² = <em>r</em> ² (<em>r</em> ² - <em>n </em>²) = <em>r</em> ² (<em>r</em> - <em>n</em>) (<em>r</em> + <em>n</em>) = 0
with roots <em>r</em> = 0 (multiplicity 2), <em>r</em> = -1, and <em>r</em> = 1, so the characteristic solution is

For the non-homogeneous equation, reduce the order by substituting <em>u(x)</em> = <em>y''(x)</em>, so that <em>u''(x)</em> is the 4th derivative of <em>y</em>, and

Solve for <em>u</em> by using the method of variation of parameters. Note that the characteristic equation now only admits the two exponential solutions found earlier; I denote them by <em>u₁ </em>and <em>u₂</em>. Now we look for a particular solution of the form

where


where <em>W</em> (<em>u₁</em>, <em>u₂</em>) is the Wronskian of <em>u₁ </em>and <em>u₂</em>. We have

and so


So we have

and hence

Finally, integrate both sides twice to solve for <em>y</em> :
