Consider the following IVP: y"-10y' +9y = 5t, y(0) = -1, y'(0) = 2 Find the general solution. 5 50 +-t+ 8 (A y (t) = 31 -9t - 2e' -e 89 81 50 + -t+ 81 31 91 – 2e' B) у (1) 9 81 5 31 (c) y (t) = 81 89 81 5 31 -t?e' – e-9 + 2e -2r D y (t) = 81 89 81 |

Q: How is linear approximation used to approximate the value of afunction ƒ near a point at which ƒ and…

A:

Q: Give a vector valued function whose graph is same as y=ln (x)

A: We know that a function with the representation r→t=ft i∧+gt j∧ is called a vector valued function…

Q: Use L's Hospital's rule

A:

Q: Illustrate Divergence in three Dimensions?

A: Divergent vector field. Three-dimensional vector field used to illustrate fluid flow with positive…

Q: if y = secx prove that y^2+y=2y^3

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: Given an Transform of a function f(s). Find x equation L-(f(s)) = xLf (s - a)} where L^-1 is the…

A: To solve the Laplace and inverse Laplace equation using formulas.

Q: Find the inverse Lapace Transform    L^(-1) {1/[(s^2 +9)^2]}

A:

Q: Describe a technique for solving a set of data's numerical derivative. Include the nature of hae…

A: There are several techniques that can be used to numerically compute the derivative of a set of…

Q: 12. [Kaplan & Glass(1995)] Limpets and seaweed live in a tide pool. The dynamics of this system are…

A: Question: The system of the differential equation is dsdt=s-s2-sl dldt=sl-l2-l2 Objective is to find…

Q: とゃ + sinhixe[ 」 sa sequence %3D メレ of functon. allacx) is seauance of function L divergent or…

A:

Q: find the inverse Laplace transform of the given function of 4e^(-2t) / (s(s+4))   Thank you for…

A:

Q: Find the image of the following lines/curves y=(1/x) under the mapping f(z) = z^2. If possible,…

A: Given y=1x fz=z2  we know z = x+iy

Q: et secydx + sinydy = 0

A:

Q: lim 3 2y ソ→o ソーSiny -sin.

A:

Q: What is the Laplace transform of f(X)=e^(-6x)

A: Calculate Laplace transform: ∫0∞fxe-sxdx=∫0∞e-6x·e-sxdx                       =∫0∞e-s+6xdx…

Q: I need to integrate 1/(sqrt(a^2+x^2)). If I let t=x+sqrt(x^2+a^2) where t>0, then how do I…

A: The given integral is,

Q: What is Lagrange's theorem?

A: Lagrange theorem is one of the central theorems of abstract algebra. It states that in group theory,…

Q: H (w) s (+リ? (outて)

A: The given problem is to find the inverse Fourier transform of the given function, we have to split…

Q: Find the unit vectors that are parallel to the tangent of the polynomial y= x^3 +2x + 1 at the point…

A: Consider the given function and differentiate to get the slope of the tangent.

Q: Find the gradient of the function whose center is at the origin and radius of 7units…

A: We have to find gradient of the function whose center is at origin and radius of 7 units. We know…

Q: can we calculate the derivative of a matrix and the nth root of a matrix ?

A: Yes, derivative of a matrix and the nth root of a matrix both can be calculated.

Q: Explain the benefit of L’Hôpital’s Rule.

A: L'Hopital's rule is the rule to determine  the limit of any given function, which is almost…