Consider the differential equation: 2y'' + ty' − 2y = 14, y(0) = y'(0) = 0.

In some instances, the Laplace transform can be used to solve linear differential equations with variable monomial coefficients.

If F(s) = ℒ{f(t)} and n = 1, 2, 3, . . . ,then
ℒ{tnf(t)} = (-1)^n d^n/ds^n F(s)

to reduce the given differential equation to a linear first-order DE in the transformed function Y(s) = ℒ{y(t)}.

Requried:
a. Sovle the first order DE for Y(s).
b. Find find y(t)= ℒ^-1 {Y(s)}

Use the distance formula to determine the distance that point q is from r on the hypotenusebased on a 2-3 ratio.i need asap !

If f(x)=3x+1 and f^-1=x-1/3, then f^-1(7)=

"curse these trig-loving pirates! " devora mutters as she looks at the map. then, after thinking for a moment, she walks back to the entrance of the secret cave, measuring 48 meters along the way. after performing a calculation, devora walks back to the empty treasure, faces the entrance, and turns a certain number of degrees to her left before walking 89 meters to the treasure. supposing that the angle at the cave entrance is acute and that devora's calculations were correct, how many degrees did she turn?