Given y₁ (t) = ² and y₂(t) = t´ satisfy the corresponding homogeneous equation of1t²y'' – 2y = − 2tª + t³, t > 0Then the general solution to the non-homogeneous equation can be written asy(t) = C₁y₁ (t) + C2y2(t) + Y(t).Use variation of parameters to find Y(t).Y(t) =

Answered: Image /qna-images/answer/3d46a007-b9ea-4497-abf0-368a67e319da.jpg

Answered: Given y₁ (t) t²y'' – 2y - = = t² and y₂…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter2: Functions And Graphs

Section2.6: Proportion And Variation

Problem 17E: Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.

See similar textbooks

Similar questions

Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.
Show that the homogenous equation(Ax + By) ⅆx + (Cx + Dy) ⅆy = 0Is exact if and only if B = C. Show that the homogenous equation(Ax2 + Bxy + Cy2) ⅆx + (Dx2 + Exy + Fy2) ⅆy = 0Is exact if and only if B = 2D and E = 2C.
Consider the equation u, uyu where u = u(x,y). (a) Use a change of variables of the form r = az, s = x+by, where a and b are constants, so that the equation becomes u, = u. (b) Use part (a) to find the solution of u, uy =u with u(0,y) = y².
I need the answer as soon as possible
Solve the non-linear DE: ² y" + (y)² = 0
ts) Find two linearly independent solutions of 2x²y" - xy + (2x + 1)y=0, x > 0 of the form Y₁ = x¹(1+ a₁ + a₂c² + a3x³ + ...) Y₂ = x²(1 + b₁c + b₂x² + b3x³ + ...) where T1 T2. Enter T1 T2 a1 = a₂ = a3 = b₁ b₂ TE b3 N - || || || || =
Let us solve the following equation via separation of variables J²u(x, t) Ət² = 3. a²u(x, t) ?х2 a) After using the ansatz u(x, t) = X(x)T(t), which equations do you get? Pick only two. (below C' denotes a constant) Ə²X(1) J²X(z) a²T(t) 842 √3CT(t) a²T(t) 84² = 1 T(t) 8²X(z) Əx² √C X(T) = C X(T) 8x² Ər² a²T(t) 3C T(t) b) We are interested in the oscillatory solution given by X(x) = a₁ cos ( $(√|C|x) + a2 sin (√√C\x) If the boundary conditions are u(x = 0,t) = 0 u(x = 1,t) = 0 Identify the correct form of the solution: O X(x) = a₂ sin(n+x) O X(x) = a₂ cos(NTT) O X(z) = a2 sin((2n-1)) = = = X(T) = OX(x) = a₂ cos((2n-1) -x)
Solve the pollowing: (1) (a) 2+j -j(xtjy) メ=? y-? 1-j (b) (2+j)(3-j2) = a+jb a:? b:? (C) (メ-j2y) -(y-jx)=2tj メ=? Y=?
Su Q: Evalute du (x-2)-
Solve the pollowing: () (a) 2+j =j(xtjy) X=? y=? 1-j (b) (2+j)(3 -j2) = a+jb a:? b=? () (x-j2Y) -(y-jx)=2tj *=? y.?
Consider the nonhomogeneous linear equation y" +9y' g(t) with the complementary solution y. = nonhomogeneous equation is of the form y, =u1 (t)Y1(t) + u2(t)y2(t)+ u3 (t)y3(t). Find the equation satisfied by the function u, (t). Ciy1(t) + C2Y2(t) + c3y3 (t). By the method of Variation of Parameters, a particular solution of the || O a. u(t) =-g(t) cos 3t O b. u(t) = 9(t) sin 3t %3D O c. u(t) = 9(t) cos 3t O d. u(t) = -9g(t) sin 3t
If y, and y₂ are linearly independent solutions of t^2y" + 5y' +(2+t)y = 0 and if W(y₁, y₂)(1) = 3, find W(v₁, Y₂) (3). Round your answer to two decimal places. W(y₁, y₂)(3) = ?

SEE MORE QUESTIONS

Recommended textbooks for you

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Given y₁ (t) t²y'' – 2y - = = t² and y₂ (t) = - 1 t = - 2t² + t³, satisfy the corresponding homogeneous equation of t> 0 Then the general solution to the non-homogeneous equation can be written as y(t) = c₁y₁(t) + c2y2(t) + Y(t). Use variation of parameters to find y(t). Y(t) =