Find the general solution of the following differential equation. Primes denote derivatives with respect to x. y² (xy' +y) (6 +x*)² = 9x .....

Q: 2. Solve the following differential equation in two ways: once using separation of variables, and…

A: Here we have to use variable separable method and reverse product rule to solve the differential…

Q: Solve for the value of "C" on the given differential equation below. Let y(1)=1 ( 3x5 + y) dx - xdy…

A: given(3x5+y)dx-xdy=0let us simplify this equation(3x5+y)dx-xdy=0dx=xdydydx=(3x5+y)xdydx-1xy=3x4this…

Q: For the following differential equation, (3D - 3D2 - 3D+ 6) y= 0. how many arbitrary constants are…

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Q: Find the complete solution for the following ordinary differential equation y" - y' - 2y = x²

A: Sol

Q: Find a general solution of the following differential equation: dy X = y + √√√x² - y² X>0 " dx using…

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Q: Find the general solution for the following differential equation: y" – 3 y' + 2 y = cos e-*

A: to find the general solution , consider the  equation y''-3y'+2y=0  the auxiliary equation is…

Q: dy :-x+2ycot2x = 0 4. dx %3D

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Q: The value of the constant a such that the given differential equation is exact ) 1 1 dx + 1 dy = 0…

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Q: Find the general solution of the following differential equation (where primes denote derivatives…

A: The given differential equation is y''+8y'+16y=0.

Q: 1. Find the solution of the following differential equation? Then find the particular solution with…

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Q: Find the value of k so that the given differential equation is exact. + kxy - 2x) dx + (3xy² +…

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Q: Find the general solution of the following differential equation. Primes denote derivatives with…

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Q: Find the general solution of the following differential equation. Primes denote derivatives with…

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Q: • Solve for the value of "C" on the given differential equation below. Let y(1)=1 2( y- 9x2 )dx +…

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Q: Find the general solution for the following differential equation, subjected to the given…

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Q: y' + }xy = sin(x 4e¤2 y3 1

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Q: Solve for the value of "C" on the given differential equation below. Let y(1)=1 ( 5x + y) dx - xdy…

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Q: Solve the following pure-time differential equation with the given initial condition. dy 2 dx where…

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Q: The following differential equation satisfies the following initial condition y(1)-0. dx X Find the…

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Q: (y2 + y)dx + (x + 2xy)dy = 0; when x=2, y=1

A: Given: y2+ydx +x+2xydy=0 ⇒dydx=-y2+yx+2xy ⇒dydx=-y2+yx1+2y ⇒1+2yy2+ydy=-dxx

Q: Solve the following autonomous differential equation with the given initial condition. dy = - 0.4y,…

A: The answer and the detailed explanation is given below-

Q: Find the general solution of the following differential equation. Primes denote derivatives with…

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Q: Obtain the particular solution for the following differential equation if y(n) = 1 (3x2 + ycosx)dx +…

A: Detail solution written below

Q: 2. Consider the following first order ordinary differential equation (x+ y) dy – (x – y) dx = 0 Show…

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Q: .. Solve the following differential equation using the indicated method. (a) y"+y' - 2y = x² + 2 sin…

A: Solution is here

Q: Find the general solution of the following differential equation (where primes denote derivatives…

A: Consider the differential equation, y''+8y'+16=0 It is a second order linear homogeneous equation.…

Q: Find the general solution of the following differential equation. Primes denote derivatives with…

A: Given DE is     3xx+6y y'=3y x-6y→     1     we have to find solution of this D.E     This is…

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: Solve the following differential equation with the given initial conditions. Indicate the method…

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Q: Find the general solution of the following differential equation. Primes denote derivatives with…

A: Given: x2y'=xy+y2

Q: Solve the following autonomous differential equation with the given initial condition. dy - 0.2y,…

A: The given differential equation is dydx=-0.2y   where  y0=70. Solve as follows. dydx=-0.2ydyy=-0.2…

Q: Solve the following differential equation using the fourth-order Range-Cata method and find the…

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Q: 1) Find the general solution to the following differential equation, (2xy? – ysin(x) + 2x + 1)dx +…

A: The given differential equation is  (2xy2 - ysinx +2x +1)dx + (2x2y + cosx +1y)dy =0

Q: 6) ( 2y - x ) dx + 3xy?dy = 0 %3D

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Q: Find the general solution of the following differential equation. Primes denote derivatives with…

A: Given D.E is         x2y' = xy + 8y2         x2y'-xy = 8y2          y'-xx2y=8x2y2       — 1 1 is a…

Q: Find the value of k so that the given differential equation is (y3 + kxy - 2x) dx + (3xy² + 12x²y³)…

A: Given differential equation is (y3+kxy4-2x)dx + (3xy2 + 12x2y3)dy = 0

Q: Find the general solution for the following differential equation: y'' -3y' +2y =cos⁡〖e^(-x) 〗

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Q: Find the general solution of the following differential equation. Primes denote derivatives with…

A: To find the general solution of the differential equation y2xy'+y5+x412=6x

Q: Find the general solution of the following differential equation:  ( 2xy + sin2x - tany ) dx + ( x2…

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Q: The appropriate integrating factor for the following differential equation (3xy + y²)dx + (x² +…

A: The given differential equation is 3xy+y2dx+x2+xydy=0....(1) We will find the integrating factor of…

Q: Find the general solution of the following differential equation. Primes denote derivatives with…

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Q: 2. Consider the following first order ordinary differential equation (x + y) dy – (x – y) dx = 0…

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Q: Find the value of k so that the given differential equation is exact. (y³ + kxy4 - 2x) dx + (3xy² +…

A: Given differential equation is (y3+kxy4-2x)dx+(3xy2+20x2y3)=0

Q: 1) (v' +x ) dy х) dx 2 1

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Q: Solve for the value of "C" on the given differential equation below. Let y(1)=1 (9x + y) dx - xdy =0

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Q: For the following differential equation, determine whether the given point is an ordinary point or a…

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Q: Solve the following Exact/Inexact Differential Equation. If it is inexact, then solve it by finding…

A: Given: 2xy-3dx+x2+4ydy=0; y1=2 Let P=2xy-3, Q=x2+4y Therefore, Pdx+Qdy=0 Now, dPdy=2x, dQdx=2x…