II. Test for exactness. If it exact, solve. 1. (x- 2y)dx – (2x + 5y)dy = 0 2. (4x³y-18x² + y)dx+ (x* +3y² + x)dy = 0 3. 2e" cos 2xdx + (e" sin2x + 3ysec y²)dy = 0 4. (3x°y+2ey +3)dx + (x³ + 4xe²s – sech y +2 1n y¯)dy = 0 5. [cos(x+ y) + cosy-3x*]dx + [cos(x + y)– xsiny+ e(y+1)]dy = 0

Q: Solve the given initial value problem: sin(2x) dx + cos(3y)dy = 0, y (Do not need to solve for y.)

A: We have to solve the given initial value problem…

Q: Given 2(dy/dx)+3y=sin⁡2x,y(0)=6 and using undetermined coefficient method: What is the complementary…

A: We have to find  the complementary solution, yc using undetermined coefficient method.

Q: se the method of undetermined coefficients to find the general solution to: y'' + y = 5 Cos(t)

A: Use the method of undermined coefficient to find the general solutionof differential equationy''+y=5…

Q: 5 dx Find dx, x> V25x? -9 5x In 25x2-9 + C 3. sin-13x+c 1+9x2 +3x|+c 1 V1+9x? + C 3x 3. + C V25x2 -9…

A: The solution is given below in the next step:

Q: 6. 3+(e*+3) sin x y tan(x³)-x

A: Solve by differentiation

Q: Find the particular solution : y" + y" +4y sin2x sin2x (b) Yp =sin2x (a) yp = - (c) Yp =- cos2x ()…

A:

Q: 3x dy dx solve +6 + 13y = 8e" sin2x - dx

A:

Q: Find a general solution to the equation y′ − 3y = e^x sin(2x).

A:

Q: Q1) Solve 1 + cos y – 2xy) dx – (xsin y + x²)dy = 0 +1

A: Given differential equation is  1x2+1+cosy-2xydx-xsiny+x2dy=0 This equation can be written as…

Q: 2e**+11e3x+16e²x V. e2x+5ex+6 sin2x vi. S -dx cosx+cos*x-2cos²x

A:

Q: i) Solve: (1+ydx = (tan-y-x)dy. %3D ii) Solve; ylogydx + (x- logy)dy = 0.

A:

Q: 1. Determine the general solution of this equation in terms of C ( sin y- ysin x) dx + (cos x + x…

A: We have the following solution for given ODE:

Q: dy +xsin 2y = x cos² y. dx Solve the Bernoulli equation.

A: Given: y' + xsin2y = x3cos2y ⇒y' + 2xsinycosy = x3cos2y ⇒y'sec2y + 2xtany = x3 Now, let tany = v ⇒…

Q: 1) If y = (x − a)√2ax - x² + a² sin−¹(*—ª),t ), then y'= 2√2ax-x² a is constant.

A: As per instructions, Here is the answer of question 1

Q: (2xy-tany)dx+(x^2-xsec^2y)dy=0 solve using exact equations

A:

Q: What is the solution of the D.E y"- 3y' = e* sinx when solved using the | method of undetermined…

A: We need to find the solution of the given differential equation using the method of undetermined…

Q: b. (1+y²)y" + xy' - 3y = cos x solve and show that this equation is non- linear and non-homogeneous.…

A: As per the question we have to use the solution of the given second order differential equation to…

Q: Given: (2xsinycosy-x+2x2eyx^2)dy=(y-sin2y-4xyeyx^2)dx Show the complete and detailed solution of…

A:

Q: Number 23

A: we have to find definite intregral of given question

Q: 2.4 sin x2 x2 +4 Find the approximate value of the integral dx by using one of the Closed Newton…

A: The given integral is ∫22.4sin x2x2+4dx We will use the trapezoidal rule.…

Q: Solve linear DE  (D2+2D+2)y=e-x+sin2x

A:

Q: 3e" + 3x + 10 cos x + 2)dx .2

A:

Q: x'y" + 2x²y" = x +sin (In x) Find the general solution of the Cauchy-Euler equation.

A:

Q: solve linear DE (D2+2D+2)y=e-x+sin2x

A:

Q: Q1: Solve by using Euler's Method. dy = x + cos(y) ; 0 <x<1 ;y(0) = 1 ; h = 0.5 dx

A: If dydx=fx, y, yx0=y0 then Euler's method states that  yn+1=yn+h·fxn, yn Given : h=0.5, x0=0, y0=1,…

Q: 4. Find a general solution to the equation y' – 3y = e" sin(2x). -

A:

Q: 2:Solve: cos (x+ y) dy = dx %3D

A:

Q: f sinh3³ x dx Ocosh³z-coshz+C O3 cosh³r+C 3 Ocosh³z + cosh 2+ C Ocosh³ +C O None of the choices

A:

Q: y" + 3y' + 2y = e* (t2 + 1) sin(2x) + 3e- cos x + 4e"

A: Answer

Q: 3 /2 pr /2 T cosy sin2x dy dx

A:

Q: (27) Solve (1+y²) | n = (tan'y-n)·dy

A: The general solution geometrically represents an n-parameter family of curves.

Q: Solve by finding an I.F 1. xdy – ydx = (x² + y² }£x y - sin x 2. dy + -dx = 0 ......

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: B) Find dx dzy and if x = sin 3z and y = tan23z dx2

A:

Q: Q5) Solve dx dx +2xy = 3 by using Euler's method to find the approximate solution up to X-2.9 when h…

A: The solution is given below

Q: 2) I = fe-zx sin 2x dx

A:

Q: -Solve b exact (Di sferential Egmation) Q 1- (3X+y Cosx) dx+(stux-uy)dy=o

A:

Q: 2. Solve the DE: 2y' - y= 4 sin( 3x)

A:

Q: Q-4) Find the general solution of the Cauchy-Euler equation x'y"+ xy'+4y = sin(In x)

A: Solve the Cauchy Euler differential equation

Q: Q1:- Solve the following DEs:- ху?-cos x sin x 1) y' У(1-x?) 2) (-4y + e-3*)dx = 4 dy -Зх dy 3) +…

A: We have to solve the given differential equation Here I am giving answer of 1st question if you want…

Q: 1 S (4x4 – e3* + cos(2x) – + 5* ) dx - x-1

A: First you need to go through the formula of calculus. Specially go through the details of the…

Q: 4) e (). – | T|x² – 4| CoS - 2 2x sin sin² ( T|x² 19 dx 2 -3

A: Integrate

Q: 3.) Solve the equation using discontinuous function: y" + 9y = cos(2t) – U37(t)cos(2t) , y(0) = 0,…

A: We will find out the required solution.

Q: Find dy/dx of: x3 - sin y = (1/x3) + tan-1 (ey) - π/4 Don't simplify the final answer.

A: Given:     To determine:

Q: cosh x Q4) Solve the initial value problem y'= y(0) = in explicit form. 3 sin y

A:

Q: Find the general solution using the method of undetermined coefficients. y'' + 3y' - 2y = -e(2x) (5…

A: It is given that y\'\' + 3y\' – 2y = –e(2x) (5 cos 2x + 9 sin 2x)        …… (1)Consider y\'\' + 3y\'…

Q: Find the General and Particular solution of = 8 sin 4x ; y= 6 when x = 0 dx Find the General and…

A: The given equations,1.dydx=8 sin4x ; y=6 when x=02. dydx=4y ; y=3 when x=0

Q: A particle moves such that its velocity at time t is given by: v = 3t2i + 2 cos(4t)j + t2k If its…

A: given velocity of the particle at time 't' v=3t2i+2cos4tj+t2k initial position x(0)=2i

Q: 24.3 Use the shooting method to solve dy - y+x= 0 2. dx2 dx with the boundary conditions y(0) = 5…

A: The complete solutions are given below

Q: Find the solution to the initial-value problem. dy dx = y2ex sin(7x), y(0) = 1 y

A: We will solve the given differential equation as shown below