Verify that y1 = x and y2 = x ln x are solutions to x 2y ′′ − xy′ + y = 0. b) use the wronskian to show that y1 and y2 are linearly independent. c) find the particular solution to the differential equation with initial conditions y(1) = 7, y′ (1) = 2

a. Substitute the given solutions and their derivatives into the ODE.

Both solutions satisfy the ODE.

b. The Wronskian determinant is

so the solutions are indeed independent.

c. The ODE has general solution . Then with the given initial conditions, the constants satisfy

So the ODE has the particular solution,

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

step-by-step explanation:   divide the numerator by the denominator to get the decimal

it would still be 193

if divide by 100 then 1.93

i am not sure