2. Consider the Bernoulli equation 5 y – 7, y(0) = 1. The substitution v = y'-" which transforms the Bernoulli equation into the first order linear equation for v. (a) Find n and v. (b) Find the linear equation for v. (c) Find the general solution for v. (d) Using the initial condition y(0) = 1 to determine the coefficient in v. %3D (e) Find the unique solution y(x) to the initial value problem.

Q: y′=y,y(0)=1

A: Use dy/dx in place of y'Then separate the variables.

Q: y' = y tan x – y² sec x

A: a. The given problem is                        y'=ytanx-y2secx ; x∈0,π2

Q: [4 .3) Use the exponential method to find the FM for the system: y' = 0 Lo -2 4 0 01 -2 y 4]

A:

Q: 2. Find a homogeneous linear equation with real, constant coefficients that is satisfied by: y = 6 +…

A:

Q: Change of variables in a Bernoulli equation The equation y'(t) + ay = by", where a, b, and p are…

A:

Q: Solve this separable equations starting from y(0) = 2:  (1 + x)y′ = 2y

A:

Q: find the general solution of the given equation. y'' + 16y = 0

A: Given , y''+16y=0Lrt , y=Aemx≠0be the trial solution of the given differential equation .Then…

Q: Use the method of undetermined coefficients to find a particular solution to the given higher-order…

A: here we only need to find particular solution which is easily done by initial guess of particular…

Q: y? + 3xy Solve the IVP y' y(1) = 5 using appropriate substitution. x2

A:

Q: find the general solution of the given equation. y'' + 25y = 0

A:

Q: y′ = −y(5 − y)

A: Recall the following fact.

Q: 3. Show that the equation (6ry – y*)dx + (4y + 3x² – 3xy²)dy = 0 is exact. Hence solve the equation…

A: Solution:

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y (4) +…

A: Introduction: The method of undetermined coefficient is a method to determine the particular…

Q: tY"(t) + (1 – 2t)Y'(t) – 2 Y(t) = 0, Y(0) = 1, Y'(0) = 2 %3D

A:

Q: Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable…

A: We have to solve this given bernouli equation.

Q: Consider the transformed cubic f(2) = (r – 1) – 125

A:

Q: tan(r) y" + ?V + y =

A:

Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx = x* +…

A:

Q: 1. Describe and solve each first-order equation. 2 2 (a) x²y'=xy²+3y² (b) y'+3y=3t²e-30

A:

Q: The following second-order equations explicitly contain y. Solve using the substitution v = y' (e)…

A:

Q: Given the Lagrange equation (1-x²)y"- 2xy' + a(a+1)y = 0 Show that x = 0 is an ordinary point. Find…

A:

Q: The roots of the characteristic equation of (D2 – D + Dy3 0 are 11 = 2 + 3i and A2 = 2 - 3i.

A:

Q: S. The transfer function of a system is given by Y(s) Gs) = 6. X(s)+ 5+2 Find the differential…

A:

Q: Solve the equation. (x+ 9x*y*) dx+ e*y°dy = 0 An implicit solution in the form F(x,y)3D C is (Type…

A:

Q: The following second-order equations explicitly contain y. Solve using the substitution v = y' (a)…

A: Solution:

Q: 2. Find the general solution of the ODE: y(4) - 8y' = 0.

A:

Q: 1. Find using Method of Undetermined Coefficient (MUC): y(3) + y(2) + y(a) + y = 2e-2* – 4x° + cos…

A: 1. Given : differential equation         y3+y2+y1+y=2e-2x-4x2+cos3x, y0=-3, y'0=-1, y''0=2…

Q: Find a particular solution y, of the following equation. Primes denote the derivatives with respect…

A: