Question

In: Advanced Math

Determine which of the following pairs of functions y1 and y2 form a fundamental set of...

Determine which of the following pairs of functions y1 and y2 form a fundamental set of solutions to the differential equation: x^2*y'' - 4xy' + 6y = 0 on the interval (0, ∞). Mark all correct solutions:

a) y1 = x and y2 = x^2

b) y1 = x^2 and y2 = 4x^2

c) y1 = x^2 and y2 = x^3

d) y1 = 4x^2 and y2 = x^3

e) y1 = [(x^2)+(x^3)] and y2= x^3

Solutions

Expert Solution


Related Solutions

a) verify that y1 and y2 are fundamental solutions b) find the general solution for the...
a) verify that y1 and y2 are fundamental solutions b) find the general solution for the given differential equation c) find a particular solution that satisfies the specified initial conditions for the given differential equation 1. y'' + y' = 0; y1 = 1 y2 = e^-x; y(0) = -2 y'(0) = 8 2. x^2y'' - xy' + y = 0; y1 = x y2 = xlnx; y(1) = 7 y'(1) = 2
Find two integer pairs of the form (x,y) with |x|<1000 such that 22x+28y=gcd(22,28) (x1,y1)=( (x2,y2)=(
Find two integer pairs of the form (x,y) with |x|<1000 such that 22x+28y=gcd(22,28) (x1,y1)=( (x2,y2)=(
a) Verify that y1 and y2 are fundamental solutions of the given homogenous second-order linear differential...
a) Verify that y1 and y2 are fundamental solutions of the given homogenous second-order linear differential equation b) find the general solution for the given differential equation c) find a particular solution that satisfies the specified initial conditions for the given differential equation y'' - y = 0 y1 = e^x, y2 = e^-x : y(0) = 0, y'(0) = 5
a) The functions y1 = x^2 and y2 = x^5 are two solutions of the equation...
a) The functions y1 = x^2 and y2 = x^5 are two solutions of the equation x^2 y ″ − 6 x y ′ + 10 y = 0. Let  y be the solution of the equation x^2 y ″ − 6 x y ′ + 10 y = 3 x^5 satisfyng the conditions y ( 1 ) = 0 and  y ′ ( 1 ) = 1. Find the value of the function  f ( x ) = y ( x )...
Find the solution of the following nonhomogeneous linear system y1′ = y2 + 1 , y2′...
Find the solution of the following nonhomogeneous linear system y1′ = y2 + 1 , y2′ =−y1 + t.
Question 1 A) Show that the functions y1(t) = 1 + t 2 ; y2(t) =...
Question 1 A) Show that the functions y1(t) = 1 + t 2 ; y2(t) = 1 − t 2 are linearly independent directly from the definition of linear independence. B)Find three functions y1(t), y2(t), y3(t) such that any two of them are linearly independent but three of them are not linearly independent.
(1 point) In general for a non-homogeneous problem y′′+p(x)y′+q(x)y=f(x) assume that y1,y2 is a fundamental set...
(1 point) In general for a non-homogeneous problem y′′+p(x)y′+q(x)y=f(x) assume that y1,y2 is a fundamental set of solutions for the homogeneous problem y′′+p(x)y′+q(x)y=0. Then the formula for the particular solution using the method of variation of parameters is yp=y1u1+y2u2 where u′1=−y2(x)f(x)W(x) and u′2=y1(x)f(x)W(x) where W(x) is the Wronskian given by the determinant W(x)=∣∣∣y1(x)y′1(x)y2(x)y′2(x)∣∣∣ So we have u1=∫−y2(x)f(x)W(x)dx and u2=∫y1(x)f(x)W(x)dx. NOTE When evaluating these indefinite integrals we take the arbitrary constant of integration to be zero. In other words we have...
The set R^2 with addition and scalar multiplication defined by (x1, y1) + (x2, y2) =...
The set R^2 with addition and scalar multiplication defined by (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2) c(x1, y1) = (cx1, y1) is not a vector space. Determine which axiom fails and find a counterexample that shows that it fails.
Determine whether the following pairs of functions are linearly independent or not on the whole real...
Determine whether the following pairs of functions are linearly independent or not on the whole real line. Determine whether the following pairs of functions are linearly independent or not on the whole real line. BEWARE: You only get 3 tries. Linearly dependent * 1. f(theta) = 14 cos 3theta and g(theta) = 56cos^3 theta - 42 cos theta. Linearly dependent  2. f(t) = t^2 + 14t and g(t) = t ^2 - 14t Linearly dependent  3.f(t)=t and g(t)=|t|
Which of the following pairs of elements are likely to form an ionic or a molecular...
Which of the following pairs of elements are likely to form an ionic or a molecular compound? Why? A. Calcium and Bromine B. Iron and Oxygen
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT