6. Solve the initial value problem y" + y = f(t), y(0)=y'(0) = 0, (21 if 0 <1 <1 where f(t)=- if t > 1

Q: In Bernoulli equation y' - xy = xy³, the value of 1(x) is ex² False True O

A:

Q: max value for y

A:

Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

A:

Q: 6. If g(x) = x'+x²+ g"(2). find the value of

A: see 2nd step.

Q: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: D. Exponential shipting Theorem (D°+ 10* - 30 - 18) y = 24 x ° e-s* -3x 4.

A:

Q: Find the general and particular solution of the y"=3e³x if f(2)= k and f'(2)=k²

A: y"=3e³x if f(2)= k and f'(2)=k²

Q: If h(2) = 4 and h'(2) = π, find g'(2) where g(x) = 2x h(x) + cos(x)

A: To find out the derivative of the given function.

Q: 3. Given f(4) = 1, f'(4) = 3, g(4) = -2, g'(4) = -5. %3D %3D If h(x) (2x3+1)f (x) Vxg(x) calculate…

A: Given that, hx=2x3+1fxxgx Differentiating with respect to x we get,…

Q: dy For each of the following functions determine dr

A:

Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 3e* Y,(t) =|

A: The given differential equation is  y"-y'-6y=3e3t  We have to find the particular solution of the…

Q: If x' x= [(-₁)] and x(0) = [] x what is X(T)?

A: Given: x'=01-10x and x(0)=01. To find: x(π)

Q: . If F(x)=√√√4t² + 1 dt, find F(2), F'(2), and F"(2).

A:

Q: If f(x) = then ƒ"(x)= = x S² (t³ + 4t 0 (t³ + 4t² + 6) dt SI

A: given,  f(x)=∫0x(t3+4t2+6)dtwe know→(i)  ∫xndx=xn+1n+1+c(ii)  d dx(xn)=nxn-1(iii)  d dx(constant)=0

Q: 1. Find the solution and the interval of validity for the following initial value problem: S# = (1–…

A: Since the initial condition is given so interval for solution is start from 2

Q: 8. The velocity of a particle moving along a straight line at time t is given by v(t) = 2t – 2t3/2 –…

A:

Q: 2. Solve y" + 2y' – 3y = 3, y(0) = y'(0) = 1. II %3D %3D

A: given differential equation is linear non homogeneous differential equation with constant…

Q: If y = (3x+8)x, compute y'(1). y'(1) = X

A: We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x The Product rule:…

Q: Solve []-[*一- -15 a'(t) y'(t) z'(t) 1009 1000 x(t) y(t) z(t) 500 2 500 400 12 1000 400 with…

A:

Q: ts1 Solve for (1+t2)y' + 4ty = f(t), y(0) = -3/4, with f (t) = { _ t 1

A: Solve

Q: solve y" - ay't ay when t=0. 11 = cost; y(t) = 1, y '(t) = 0

A:

Q: Find y' implicitly. 1. (x + y)² = 4y 2. (x + 2y)² = x + 10 of 1

A:

Q: The population of elk in a national park is given by the function 1000 P(t) = 1+15e-3t where t is…

A: This question can be solved using the concept of differentiation and limits.

Q: Find the stationary points and stationary values of the function f (x)=2x'+x² - 20x +5.

A:

Q: 8. Solve 2y"+y' = g(t); g(t) = (4t; t < 1, 16;t ≥ 1:y(0)=-6, y'(0)=1

A: Sol:- First write g(t) in terms of unit step function :- gt=4tt&lt;16t≥1gt=4t*Ht-Ht-1+6Ht-1Now , we…

Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0