To verify: Whether the functions y 1 ( x ) = x − 1 2 sin x and y 2 ( x ) = x − 1 2 cos x satisfies the corresponding homogeneous equation of the differential equation x 2 y ″ + x y ′ + ( x 2 − 0.25 ) y = g ( x ) , x > 0 and compute the particular solution.

Question

Want to see the full answer?

Answer 1

Question

Chapter 3.6, Problem 15P

To determine

To verify: Whether the functions y1(x)=x−12sinx and y2(x)=x−12cosx satisfies the corresponding homogeneous equation of the differential equation x2y″+xy′+(x2−0.25)y=g(x), x>0 and compute the particular solution.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

5. (20%) The linear transformation L: P3 → P2 defined by L(f(x)) = f'(x)+ f(0). (a) Find the representing matrix A of L with respect to the ordered basis {x2, x, 1} for P3, and the ordered basis {2,1 - x} for P2. (b) Find the coordinates of the f(x) = 2x² +2 in P3 with respect to the ordered basis {x2,-x, 1}, and find the coordinates of L(f(x)) with respect to the ordered basis {2,1-x}

One hundred students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey. Preference Male Female TOTAL Prefers dogs \[36\] \[20\] \[56\] Prefers cats \[10\] \[26\] \[36\] No preference \[2\] \[6\] \[8\] TOTAL \[48\] \[52\] \[100\] problem 1 Find the probability that a randomly selected student prefers dogs.Enter your answer as a fraction or decimal. \[P\left(\text{prefers dogs}\right)=\] Incorrect Check Hide explanation Preference Male Female TOTAL Prefers dogs \[\blueD{36}\] \[\blueD{20}\] \[\blueE{56}\] Prefers cats \[10\] \[26\] \[36\] No preference \[2\] \[6\] \[8\] TOTAL \[48\] \[52\] \[100\] There were \[\blueE{56}\] students in the sample who preferred dogs out of \[100\] total students.

For the spinner below, assume that the pointer can never lie on a borderline. Find the following probabilities. (enter the probabilities as fractions)