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,

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.

i can not answer the question due to the fact that you spelled "carton" as "cartoon", a cartoon is something you watch on tv, a carton is a box that holds things. and also you've been waiting for this question for a while so why don't you get off your lazy a** and try to figure it out for yourself for once!

step-by-step explanation:

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look above, and leave your comments down below, and don't for get a five stars and a and brainliest xd

sorry for the stars in the middle of words its because it wouldn't let me submit. xd