Decide first if the following Differential equation is exact. If exact then find the solution (r – y3 + y? sin r)dr = (3ry² + 2y cos r)dy

Q: given the differential equation dy/dx +y^2 = sin(2x) with initial condition y(0)=1 find the values…

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Q: SOLVE THE FOLLOWING DIFFERENTIAL EQUATIONS. 1. siny dx + (x - sin? y)dy=0 2. x + ( 1+x)y = e -x…

A: As per our guidelines we are supposed to answer only first one. Then i solve Question (1) . Please…

Q: Find the solution of the following differential equation. 1. (e" + In y +) dx + ( + In x + sin y) dy…

A: Solution of the differential equation

Q: Find the solution of the following differential equation. 1. (e" + In y + ") dæ + ( + In x + sin y)…

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Q: 1. siny dx + (x - sin? y)dy=0 + ( 1+x)y = e -x sin2x

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Q: Find the solution of the following differential equation. 1. sin 3ædx + 2y cos³ 3ædy = 0

A: Firstly separate the variables and then integrate . dsecaxdx =a tanax secax ∫xn dx = xn+1n+1+C

Q: Show that given differential equation is exact and hence solve it (y sin z)dr - (y+y+ cos a) dy = 0,…

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Q: Q2: Solve the following differential equations cos y dx + (xsiny - cos'y )dy = 0 cos y )dy = 0

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Q: Find all values of k for which the function y = sin(kt) satisfies the differential equation y' + 17y…

A: We find y" using the chain rule

Q: SOLVE THE FOLLOWING DIFFERENTIAL EQUATIONS. 1. siny dx + (x - sin? y)dy=0

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Q: Solve the following Exact Differential equation. (x + sin y)dx + (x cos y – 2y)dy = 0 %3D

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Q: Find all values of k for which the function y = sin(kt) satisfies the differential equation y" + 16y…

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Q: Find the solution of the following differential equation. 1. (e* + Iny + ) da + ( + In æ + sin y) dy

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Q: Given, G+) dæ + (41) dy = 0 is an exact differential equation. Determine the value of A.

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Q: Find the solution of the following Differential Equations By Exact 19) ycos(x)dx+ 2 sin(x)dy 0

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Q: 4r³ sin 20 cos 20 dr = d0 ;r = 3,0 = 22.5° %3D

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Q: For what value of k the given differential equation is exact? (4æy – 2y)dæ + (2² – 6kxy?)dy = 0. %3D…

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Q: Given the equation sin x sin y dx + cos r cos y dy = 0. a. Determine the type of differential…

A: The given differential equation is: sin x sin y dx+cos x cos y dy=0

Q: 2(3e²* cos y + x) dx – 3e2* sin y dy = 0 ; y(-n) = 0

A: Using Method of Exact Differential Equation.

Q: Show the following differential equation is exact, then solve it. [sin(xy) + xy cos(xy) – 8x]dx +…

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Q: Find the solution of the following Differential Equations 5) sinh(x)cos(y)dx = cosh(x)sin(y)dy %3D

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Q: (b) Determine whether the given differential equation is exact. If it is exact, solve it. ) dy +…

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Q: Solve the given differential equation subject to the indicated conditions. y" - 4y = x + sin x, y(0)…

A: The given differential equation is y''-4y=x+sin x, y0=5, y'0=2y

Q: SOLVE THE FOLLOWING DIFFERENTIAL EQUATIONS. 1. siny dx + (x - sin? y)dy=0 2. x + ( 1+x)y = e -×…

A: First order differential equation : Consider the first order differential equation…

Q: 8. (6xy + cos s y) dx + (2kxy² – x sin y) dy = 0 %3D

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Q: Solve for the value of "C" on the given differential equation below. Let y(1)=1 ( 9x5 + y) dx - xdy…

A: We first rearrange the given differential equation and write it in other form as

Q: Determine if the following Differential Equation is an Exact/Inexact. If it is an inexact…

A: Exact differential equation: A differential equation M dx + N dy = 0 is said to be exact if…

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: (2a+y)dz + (a'y– a) dy = 0 %3D

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Q: Find the solution of the following differential equation. 1. (e" + In y + ) dæ + ( + In æ + sin y)…

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Q: y' = x sin? y Ans: 2 cot y – x² = c

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Q: Suppose y cos 0sin 0. Answer the following. dy de 6) Separate the differential equation, then…

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Q: Given : (e* + In y + 2)dx + Š + In x + sin y )dy = 0 Find the general solution for this differential…

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Q: (y² cos x – sin x)dx + (2y sin x + 2)dy = 0 (Exact)

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Q: Decide first if the following Differential equation is exact. If exact then find the solution z(1 –…

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Q: Find the solution of the following Differential Equations 5) sinh(x)cos(y)dx = cosh(x)sin(y)dy 7)…

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Q: Find the solution of the following differential equation. 1. (e + In y +) dx + ( + In x + sin y) dy…

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: verify that the given differential equation is exact; then solve it. 37. (cos x + In y) dx +(÷+e" )…

A: Given, the differential equation is Verify that the differential equation is exact and then find…

Q: Solve the following linear differential equation 1. y''+y'=-cos x 2. y''-6y'+9y =ex

A: we have to solve differential equation

Q: y' = cos?x cos y %3D

A: Explanation of the answer is as follows

Q: Find the solution of the following Differential Equations 5) y'+y=sin(x) 7) y+ky = e

A: 5. y'+y=sinx 7. y'+ky=e-kx   “Since you have asked multiple questions, we will solve the first…

Q: Show that the given differential equation is not exact hence solve it æ?ydx – (x³ + y³)dy= 0 %3D

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Q: The following equation is not exact but it can be changed into exact differential equation (x +…

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Q: Find the solution of the following differential equation: dy + 3y : sin(x)

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Q: equation

A: Given is the differential equation (x5 + 3y) dx – 9 xdy =0 with y(1)=1. The objective is to find the…

Q: Solve the given differential equation. Ans: + cos x = c 1. y' +y2 sin x = 0 %3D y

A: The objective of the question is solving the differential equations.

Q: 1. siny dx + (x - sin? y)dy=0

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Q: Find the general solution of the following differential equation: (sin x)y' + (cos x)y = ex Then…

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