(3) Solve the exact initial value problem 1 √y+3 y(y + sin x) dx + 2xy - cos x + leaving the solution in implicit form. dy = 0, y(0) = 1,

Q: Solve the initial value problem y dy/dx = sin 2x ; y(0)=2

A:

Q: Find the general solution of y"+y = cos(t) (a) Using undetermined coefficients (b) Using variation…

A: Find the general solution of (a) Using undetermined coefficients.(b) Using variation of parameters.

Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

A:

Q: 6. Solve y sin (x) cos (x) with initial condition y'(7) = 1 and y(7) = 0.

A: y = 1/4 [ x - 1/2 sin2x] +x -π/4

Q: Solve y′′ − 2y′ + y = 2sinx − cosx  , y′(0) = 0 , y(0) = 0

A:

Q: y(7) −4y(6) −4y(5) + 56y(4) −156y(3) + 224y'' −176y' + 64y = ex cos(x)−3e2x + xe−4x What is the…

A: y(7) −4y(6) −4y(5) + 56y(4) −156y(3) + 224y'' −176y' + 64y = ex cos(x)−3e2x + xe−4x

Q: Find the general solutions (implicit or explicit) to the following equations. (a) y' = e3x-2y + x²…

A: First order ordinary differential equation.

Q: Show that an implicit solution of 2x sin?(y) dx – (x² + 16) cos(y) dy = 0 is given by In(x? + 16) +…

A:

Q: (D2 -3D+2) y = e sin (e") - 2

A:

Q: Solve (x + sin(y))dx + x cos(y)dy = 0 and find the solution passing through (2,7)

A: Given: We have to solve the given differential equation and find the solution passing through

Q: Find the directional derivative h(x, y, z) = cos xy + e" + Inzx. P (1,0,0. 5) A= 1+2]+2k

A:

Q: A regular eustomer visits a restaurant thrice a week. For a monthly visit, he wants to try something…

A:

Q: (h) xy" + 8y' +18xy = 0, xo = 1 (i) (3 — x²)y" — 8xy' - 18y = 0, xo = 0 (j) 2y" + 8xy' + 18y = 0, xo…

A:

Q: (b) Solve the following initial value problems: (2xy-9x²)+(x² + 2) t+2y-2 +3 sint; (1) = 0; y(0) = 3…

A: Solution of the initial value problems

Q: Find a particular solution using the Undetermined Coefficients Method of y" -y' + y = 2 sin3x.

A:

Q: (1) Integrate the following functions: (a) I = [ (4x³ − 6x² + 2x²³¹′)dx (²-3)dx 2 (b) I = .3 (c) I =…

A:

Q: Determine the most appropriate method to find the general solution for the functions: y" - y' - 2y =…

A: Given differential equation is y''−y'−2y=2x+sin2x−4hcos2x. We have to determine the most appropriate…

Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO F

A: Topic- Derivative

Q: Solve  y′ + 2y cos(2t) = 2 cos(2t), y(π/2 ) = 0

A:

Q: Solve using the method of undetermined coefficients: y" + 8y' = 2x¹ + x²e-³x + sin (x)

A:

Q: Solve y"-4y+Sy=mxe'sin(x)+(m+3)cos(x) by the method of undetermined coefficients.

A:

Q: Solve. y" + 6y (v¹)³=0 a. v(x) = C₂e1*-6 C₁y+y³=C₂ + x b. C. (C₂-y)² + x² = C₁ d. y=C₂-In(C₁-x²) e.…

A:

Q: - Sapotri to solve 2x?y" – my + (x + 1)y = 0. n=0 12) Use y =

A: Given: 2x2y''-xy'+x+1y=0. To Do: Solve the given differential equation using y=∑n=0∞anxn+r.

Q: Solve y'+by+9y = 0, y(0) = −2, y'(0) = 7 y(t) =

A: Given :

Q: form.

A: The given differential equation is not exact .And the solution is:

Q: Find the general solution of the x²y" + xy' − y = 3x, x‡0;

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: (b) _x²y″ − 2xy' + (x²+2)y = 0, given solution y₁ = x sin x -

A: (b) The differential equation is given as , x2y''-2xy'+x2+2y=0              .....1

Q: 1. Solve the initial value problem on the real line Utt - Uzz = sin x xx U(x,0) = 0 Ut(x,0) = sin x

A: