Answer the following two questions. 1. Solve the following differential eauations with the given initial or boundary con- ditions. (a) For boundary conaitions y = 1 at r = 1: + 3ry = 4r. dr (b) For initial conditions z = 0 at t = 0: dr + br = Atet, dt

Q: -3(4x + 3)+ 4(6x+1) = 43 %3D

A:

Q: 1. An object is moving along a straight line and its velocity at time t is given b v(t) = t² − 4t -…

A: Given :- ⇒vt=t2-4t-5 By completing square method ⇒vt=t2-4t+22-22-5 ⇒vt=t-22-9 vertex (2,-9)

Q: Solve the homogenous diff equation of; y' = y sec x

A:

Q: c). i. Find the general solution to this homogeneous equation using the auxiliary equation method…

A: We will use the basic knowledge of differential equations and methods for solving them to answer…

Q: di 1. L+ Ri = E dt 2. (x + y)dx + (3x² – 1)dy = 0 | 3. x(y")3 + (y')* - y = 0

A:

Q: 8. A skydiver jumps from a plane, and up to the momeht air resistance is proportional to v³/² (v…

A: Given that v'=32-0.032v32 in the interval 0,6 with v(0)=0 The step size is h=0.05 By Euler method,…

Q: Usmo Jourth order runge - Kutta method compute y (1.5) ナ is satisfice the differential uchero…

A:

Q: 3. (a). For a curve defined by an equation f(x), satisfy dy + (1 – 2x)y = 4x for x > 0 and - dx f(1)…

A:

Q: 3. Sketch solution curves for a variety of initial conditions for dw = (w - 3)(w – 7). dt

A:

Q: This is the idea of a slope field graph: 1. Our goal is to sketch the unknown function y (t). 2. We…

A: Basic propoerties of the curve y(t). The curve y(t) touches the tangent at every point. It never…

Q: d²y =t+ cost di2 Q.4(20 Points): Find a function f(t) such that and such that y(0)%=D1 and y (0)=2.

A:

Q: e distance of the particle f

A:

Q: Usually in a method of solution for Homogeneous DE, after the substitution of y = vx (or x = vy) and…

A: In the method of solution for homogeneous differential equation, The equation is of the form,…

Q: find the differential equation for the following families of curves. 8. Horizontal parabolas whose…

A: Consider horizontal parabolas whose vertices lie on y-axis. The objective of the problem is to find…

Q: 3. Find all the first and second order partial derivative of the function: z(x, y) = sin(Mx) cos(Ny)…

A:

Q: Q5. If W = x² y + 2xyz , x = t², y = t + 1, z = 2t at t = 1. Find the total differential

A: Let's find.

Q: 1. Find the first derivative of y: y=x-6x³+2x²

A: Topic = Derivative As per guidelines , At  a time only one question can be answered. please repost…

Q: 3x y = .3 х +3x

A:

Q: If z = -1e²+3y, find the differential dz. dz= Submit Question

A:

Q: find the differential equation for the following families of curves. 11. Hyperbolas with vertical…

A:

Q: 5. Use differentials to approximate the value of V(3.01)² + 2(0.99) – 3 in four decimal places.

A:

Q: Problem 1: Using differentials, approximate the change in the total surface area of a parallelepiped…

A: We have to use total derivative to find change in surface area .  If f is a function of x and y…

Q: g8 The lartial differential equation d'u 3Q4is %3D Claddlificd as:- fa) larakolic (6) sliptic (d)…

A: Consider the equation of the type: Rr+Ss+Tt+f(x,y,z, p,q)=0 where  r=∂2z∂x2 , s=∂2z∂x∂y, t=∂2z∂y2,…

Q: For the following differential equation with parameter µ: y = y? + 4y + u a) find the bifurcation…

A:

Q: Match the following: If S(t)=t³-3t2-6t+1 then Choose... + instantaneous velocity at t= -2 is If…

A: Explanation of the solution is given below...

Q: - SolNe the fofla wing differeutial equatious using Laflace ransform methad,

A: 1. Take the Laplace transform on both sides of the differential equation.…

Q: 8. The p.d., V, between the plates of a capac- itor C charged by a steady voltage E through a…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.