Test for the exactness and find the implicit solution to [2x+ycos(xy)]dx+ xcos(xy)dy=0when -플.y=1. X = x2 + sinxy= +1 - 1 x2 – sinxy= 4 O x2 – 2sinxy= 4 4- x2 - sinxy=1

Q: Q2:- Check that the indicated functions are solutions to the given differential equation :- 1) y" +…

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: Solve the given initial-value problem. dx y - X= = 5y², x(8) = 1 dy x(y) = Give the largest interval…

A: Given that,   ydxdy-x=5y2, x(8)=1

Q: Find the general solution of the differential cquations : d2y = e2* (12 cos 3x – 5 sin 3x) dx2 2.…

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Q: I Solve the differential equatons when X= (x+y) dx +(2xy+xh 3x) dy=o 1. Y= 2

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Q: Solve the initial value problem. dy = 12 sin 2 x dx x cos x, y(0) = 3. HINT: First integrate the…

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Q: 4. Solve the initial value problem. dy a. = 3e* →, y = 6, when x = 0. dx %3D %3D

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Q: slove the initial value problem: (dx/dt)-5x=cos(4t) with x(0)=5 find x(t)

A: The given initial value problem is: dxdt-5x=cos4t with x0=5. The given differential equation is a…

Q: Solve the differential equation below over the interval from x = 0 to 1 using a step size of 0.2…

A: Given differential equation is:  dydx=x2+y,  y(-1)=0We have to solve the given differential equation…

Q: Verify that the given function y = sin (x2 + C ) is a solution of the given differential equation:…

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Q: Find the general solution of the differential equation xyl – yl – (x – 1) cos (x)+y = 0 and choose…

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Q: Solve the differential equation below over the interval from x = 0 to 1 using a step siz of 0.2…

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Q: 2. Obtain the general solution using Bernoulli's equation. Si l + x/ dx – 6x dy = 0

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Q: 3. Find the general solution of y" – 3y + 2y = cos (e~-).

A: We use the method of variation of parameters to find the solution of y''-3y'+2y=cose-x First we find…

Q: | Solve the initial value problem dy + (cos r)y 1 sin 2x, y(T/2) = 1/e. %3D dx

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Q: $(x) = sin x cos x is a solution to the initial value problem d²y +у%3D0; у(0) %3D — 1, dy - (0) =…

A: We have to solve given problem:

Q: 1. Use the substitution z = following differential equation xy, where z is a function of x, to solve…

A: Properties of integration  ∫1a2+x2dx=1atan-1xa+C∫xndx=xn+1n+1+CddxUV=UdVdx+VdUdx

Q: Find the general solution of the following differential equations. 3. (cos x cos y – cotx)dx – sin x…

A: compare given DE with Mdx + Ndy = 0  and then solve

Q: Find the solution to the Bernoulli equation. y = 2(3x+ y)2 – 1; x= 0,y=1 O 4tan-1(3x+ y) = 8x + T…

A: The solution is given as

Q: Obtain the particular solution satisfying the initial conditions indicated. 1. e* (3x°y-x)dx+e" dy =…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the general solution of (3xy-y²)dx-(x²-xy)dy=0

A: As the equation is homogeneous , put y=vx and solve .

Q: What is the general solution to the differential equation sin y (x + sin y)dx + 2x² cos y dy = 0 ?…

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Q: Solve the given initial-value problem. (x + 1) dy + y = In(x), y(1) = 25 dx y(x) = Give the largest…

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Q: Choose the correct answer for Wronskian, W for the following differential equation, y"-y=9e*…

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Q: For what positive values of k does the function y = sin(kt) satisfy the differential equation y" +…

A: Given: The function y=sinkt satisfies the differential equation y''+324y=0 . The function y=coskt…

Q: 1 Find the complete solution of y" - 2y' + 2y =x + e* cos x.

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Q: The solution of the separable differential equation – x²y² = x² is: dx None of the above…

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Q: Solve the initial-value problem cos y + (1 + e^−x)sin y dy/dx = 0, y(0) = π/4

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Q: What is the general solution to the differential equation dy = dx + 3y tan x ? sin³x y cos³x = sin x…

A: Correction : In right hand side of given differential equation is {dx + 3y tan x dx}

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

A: Given:    dydx = y2exsin(7x)       ,   y(0) =1

Q: dy-5+4y =16x+20e" dx ; y(0) = 0, y'(0) =1 dx

A: Given differential equation d2ydx2-5dydx+4y=16x+20ex. The Auxiliary equation is…

Q: (y cos x + 2xe')dx + (sin x + x²e> – 1)dy = 0

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Q: Solve the fourth order differential equation completely d*y d°(y/x) dx sin(x)+ cos(x) %3D 3 dx³

A: Given: A fourth order differential equation…

Q: Find the solution to the initial-value problem. dy dx = y2ex sin(2x), y(0) = 1 y =

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Q: dy What is the solution of the differential equation of x 2y I* cos 4x ? %D dr 4y = - sin 4r + Cr 2…

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Q: Verify that the indicated function is an explicit solution of the given differential equation.…

A: The function is given as:

Q: 1.) Obtain the general solution of the differential equation dx – (1 + 2x tany) dy = 0.

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Q: Solve the given initial-value problem. dy + y = In(x), y(1) = 20 dx (x + 2) y(x) = Give the largest…

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Q: (ysin x+xy cos x)dx+(xsin x +1)dy = 0 Ans. xy sin x+y = c

A: A differential equation of the form M(x,y)dx+N(x,y)dy=0 is said to be exact iff ∂M∂y=∂N∂x

Q: Find C co that the line y = 4x + 3 is tangent to the curve y = x2 + C.

A: We can solve it using differential equation as below.

Q: Solve the given initial-value problem. (x + 1) dy + y = In(x), y(1) = 10 dx y(x) = Give the largest…

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Q: Given the initial condition y(0) = 5, find the particular solution of the equation e'y' – 4x = 0.…

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Q: . x dy/dx - (1 + x)y =xy²

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Q: What is the general solution to the differential equation x = y + y³ cos x ? dx = -2x?(y* sin x +…

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Q: (b) d²y dy Find the solution for cos(x) ² − (1 + x²) dx − 2xy = 12 with the conditions - dx² dx 1+x²…

A: Given cosxd2ydx2-1+x2dydx-2xy=11+x2y1=-1, y2=2, h=0.25`

Q: Find the differential equation y(x – 1)dx – (x² – 2x – 2y)dy = 0 a.x² + 2x + 4 = 2Cy² b.x² + 2x + 4y…

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Q: x dx + sin? [ydx- xdy] = 0 %3D ( 3x - y + 1) dx -(9x- 3y - 3) dy = 0

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Q: 8. Solve the initial value problem: ( dy = y(y + sin x), y(0) = 1 dx + cos x – + y? 2xy

A: The given problem is to solve the given initial value problem, Firstly we have to check the…

Q: Solve the given initial-value problem. dy X- +y=6x + 1, y(1) = 7 dx y(x) = Give the largest interval…

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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

Q: Solve the differential equation below over the interval from x = 0 to 1 using a step size of 0.2…

A: We have to solve the given problem analytically.