The solution of y" = 8(t – 1) – 8(t – 3), y(0) = y'(0) = 0 is y(t) = (A) (t – 3) [u(t – 1) – u(t – 3)] (В) t(u(t — 1) — и(t — 3) (С) (t — 1) (u(t — 1) — и(t — 3)] (D) (t – 1)u(t – 1) – (t - 3)(t - 3) (E) (t – 1)?u(t – 1) – (t – 3)'u(t – 3)

Q: Obtain the differential equation of the given family of curve: y^2=x^3/(c-x) O A. 2x^3 y^'-3x^2…

A: Explanation of the answer is as follows

Q: y,(x) = ež, y',(x) = xe y" – y' + 0.25y = 0, a. Verify if the functions yı and y2 are solution of…

A: To check that a function is  a solution of a differential equation, if we substitute in the left…

Q: (a) Let f(x, y) = x2 e-y. Show that %3D ax3 ay? ay3 ax3 x+y (b) Show that the function f (t), where…

A:

Q: 1. Use the Chain Rule to find dy in term dr а у — (и— 2)3 and и - 2x + 1 b. y = Jū and u=5x² – 3 1 1…

A: In this question we will use basic of calculus i.e differentiation by using chain rule. We will…

Q: Q2) a steel plate of dimensions 4 cm x 4 cm and negligible thickness is in steady state conditions.…

A: Given- ∂2u∂x2+∂2u∂y2=0 where 0≤x≤4 and 0≤y≤4 B.C. u=0 at x=0  and u=8+2y at x=4 u=12x2 at y=0 and…

Q: Solve the partial differential equation: a²u =²; by the method of separation of variables for a…

A:

Q: B/Verify that u(x, y, z) = Tr + yk 4+z? satisfies the partial differential equation a2u a2u a2u = 0…

A: B.

Q: Given partial differential equation u, +u-xsin (t) = 4e?* ii uu, +u, +u, = 12 Based on the above…

A:

Q: ) y, = x2 IS ODE X²y"+2y-6y=0 SOLUTION OF THE USE THE REDUCTION OF ORDER FOAMULA TO FIND A SCCOND…

A: We have to use reduction formula:

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A:

Q: Use Laplace transform to solve the differential equation y"-2y'-3y=0 with the initial conditions…

A: A linear homogeneous ordinary differential equation can be solved using the Laplace transform apart…

Q: When the differential equation y" + 2 y' + y = x (e)^(- x) given y (0) = 1 and y'(0) = - 2 is solved…

A:

Q: What is the solution of the differential equation using Laplace Transform y'' - 3y' + 2y = e3x when…

A: What is the solution of the differential equation using Laplace Transform y'' - 3y' + 2y = e3x when…

Q: 9-20 Compute the differential dz or dw of the function. 17. w = x'y?z

A: Given

Q: Solve the Dirichlet problem on {x² + y² < 1} {x² + y² = 1} Au = 0 I u(x, y) = 2xy + 2y? on

A:

Q: (b) Find the general integral of the partial differential equation dz dz. = 7., X- which contains…

A:

Q: 1. Show that u(x,t)= etsin kx satisfies the partial differential equation_u₁ = α² uxx

A:

Q: () 2. If k = w3 – wv², w=xy, v = w+ x, find and using: dw a) the chain rule b) differentials.

A: Given: k=w3-wv2, w=xy, v=w+x   To find: (∂k∂w)x . (∂k∂x)w  using chain rule and differentials

Q: Show thatƒ (x, y, z) = x² + y² – 2z2 satisfies the Laplace's partial differential equation.

A:

Q: Verify that the given two-parameter family of functions is the general solution of the…

A:

Q: (х-1)у"-ху'+у-0 Yı(x)=e* y'2(t)=x a. verify if the functions y, and y2 are solution of the given…

A:

Q: at f(x,y,z) = z exp(− x2 + y2 4z ) satisfies the differential equation ∂2f + ∂2f = ∂f ∂x

A: To prove that                 ∂2f∂x2+∂2f∂y2=∂f∂z Where,         f(x, y, z)=1ze-x2+y24z

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A+…

A: In this question we need to find a derivative of the given equation.

Q: HW: Solve the Partial Differential Equations by using separation of variables method: U1 – 4uxx = 0…

A: From the given conditions, answer is not correct. Please check the whole questions and answer.

Q: A system that is initially at rest has response x(t) to an input u(t) and is described by the…

A: Sol

Q: Obtain the differential equation of the given family of curve: y² : C-x a. 2x³y' – 3x?y – y³ = 0 b.…

A: Given curve : y2=x3c-x ⇒c-x=x3y2

Q: 5) Given the system of differential equations 2 dx dy +2x-y=3t dt dt dx dy + +x+y=1 dt dt with the…

A:

Q: - Show that the partial differential equation = 0 has the general solution u(x, y) = e"[f(x) + g(y)]…

A:

Q: 2. Show that the substitution z=y(1-n) will reduce the Bernoulli Equation y' + f(x)y = Q(x)yn to a…

A: The solution is given as

Q: 4. The associated auxiliary equation with the homogeneous linear differential y"+2y' + y = 0 is A.…

A:

Q: 2) a² u(x,t) / at² = 9 d² u(x,t) / dx² (-0∞ 0) Solve the partial differential equation u(x, 0) =…

A:

Q: -171 – 60y 5z + 18y satisfying the initial conditions z(0) = 7 and y(0) = -2. Find the solution to…

A: To find the solution of the given system of differential equations, first we find the eigenvalues…

Q: Compute the nonhomogeneous linear DE. a. y" -y = x + ex b. y"- 2y + y = x’e*

A: We are given Non homogeneous differential equation. We have to find their solution.

Q: . Verify that the functions y1(x) = 1, y2(x) solutions of the differential equation xy" – y" = 0 on…

A: Given information: Differential equation xy'''-y''=0 An Euler homogeneous ODE is a form of…

Q: 1. Use the Chain Rule to find 1. y = u² + 1 dy dx (show your complete solution) . u = x² - 1

A: dydx=4x3-4x

Q: Find the differential equation of the quartics : c^2y^2 = x ( x - a )^3 with c held as fixed.

A:

Q: Solve the partial differential equation: ди + u дх ди 3 at given u(x, 0) = 7e2x -

A:

Q: 7. The solution d'y tion k² dx² of the differential equa- = y = y₂ under the boundary conditions (i)…

A:

Q: Q-1-) Eind the general solution of the given Ordinary Differential Egauations system: X'(t) = *(1)…

A: Given: X¯'(t) =3-94-3X(t) where X¯(t) =x1(t)x2(t) To find: General solution of given system of…

Q: Rewrite y" - 2y + y² = cos x as two first-order equations and then use Euler's method to integrate…

A:

Q: A dynamic system is represented by the following differential equation. y" - y' - 2 sin y = u(t),…

A:

Q: 4. Use the method of undetermined coefficients to find a particular solution to the system below.…

A:

Q: ! Find a second solution y2(r) of the differential equation y" + 6xy +6y = 0, r> 0, by the method of…

A:

Q: For the following system: dx dt dy = x – x* dt (a) Find equilibrium point(s) of the system.

A: (a)  We have given system of differential equations       dxdt=-y4       dydt=x-x3to find…

Q: What is the differential equation of the orthogonal trajectories of the family of curves X2 -…

A:

Q: a) The response of x(t) of a system towards a forcing exponential function is determined by the…

A: Let's find.

Q: 2. (a) Given that y, = x and y2 = x In x are solutions of the differential equation x²y" – xy' + y =…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.