Solve the given differential equation by separation of variables. ety dy eУ + е-5x — у dx =

Q: dy 2x + (4x + y – 6) = y dx

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

Q: solve the given differential equation. y − xdy/dx = 3 − 2x2 dy/dx

A:

Q: Solve the given differential equation. (6x + 1)y² 2 dy + 3x2 + 3x² 2y³ = 0

A:

Q: Solve the given differential equation by undetermined coefficients. y" - y' - 30y = e6x y(x) =

A:

Q: y =1+r+y+rY =D1+x-

A: A differential equation is an equation that consists of a differential coefficient in combination…

Q: Solve the given differential equation by undetermined coefficients. y" - y' +y = 5 + e/2 4 (x) = %3!

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: dy + y = ry dr

A: Given differential equation is xdydx+y=xy3 or xy'+y=xy3  First order Bernoulli Ordinary Differential…

Q: x²ydx – (x3 + y³)dy = 0

A:

Q: Solve the given differential equation by separation of variables. dy = 6y xdx dx

A:

Q: Determine all the values of m of the auxiliary equation of the differential equation, d'y = 5 da4…

A:

Q: Solve the given differential equation by separation of variables. dy ху + 5х — у - 5 dx ху — 2х + бу…

A: The solution of the provided differential equation by separation of variables is given by,

Q: Find the general solution for each differential equation.

A: The given differential equation is, dydx=3x2+ex4y3 On separating the terms, we get…

Q: Determine the degree of this differential equation: + ( - 3+y = 9 a²y ... dx3 dx2 dx None of the…

A: We know that dydx=y' and d2yd2x=y'' and so onThe given differential equation can be written as:…

Q: Solve the given differential equation by separation of variables. xy + 5x - y -5 xy - 2x + 6y - 12…

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Q: Solve the given differential equation by variation of parameters. x?у" - ху' + у %3D 8x y(x) = х> 0

A:

Q: Find the general solution of the differential equation ? y" - xy' + y = 0

A: Consider the given equation. y''-xy'+y=0 Let's the solution of the equation is y=∑n=0∞anx-an. Find…

Q: Solve the given differential equation by separation of variables. dy = e5x + 4y dx -4e5x 5 + C X

A:

Q: Solve the given differential equation. 25x?y" + 25xy' + y = 0 y(x) = ,x > 0 %3D

A: We have to find solution of given differential equation.

Q: solve the given differential equation. dy/dx = 2x y

A:

Q: Solve the given differential equation: (3x+2y) dx+(2x+y) dy=0.

A: Gievn equation -  (3x+2y) dx + (2x+y) dy =0

Q: Solve the given differential equation by separation of variables. dy 2y + 7\2 dx 8x + 9

A: If the differential equation can be written in the form of fydy=gxdx then it is called separable…

Q: Find the general solution of the given differential equation: 3t?y" + 7ty' + 10y = 0

A:

Q: Solve the differential equation. dy 9x?y2 dx

A: dydx=9x2y2 Formula ∫xndx=xn+1n+1+C

Q: Solve the given differential equation by undetermined coefficients. y" + y² + y = x² - 5x y(x) =

A:

Q: dy + 3y = 3x²e-3x dx

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Q: Solve the differential equation. dy = e5x - 5y dx

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Q: Solve for the general solution of the given differential equation ху + у? and express your final…

A: The given differential equation,y'=xy+y2x2

Q: Solve the given differential equation by separation of variables. (ey+1)2e-ydx+(ex+1)6e-xdy=0

A: Rearranging the given equation:

Q: 27. dx = 2 + Vy – 2x + 3

A:

Q: = 3y? – y²sinx dx

A: Given that: dydx=3y2-y2sinx

Q: Solve the given differential equation by separation of variables. dx + exdy = 0 y = 14e - 4x + C X

A: We can solve the given differential equation by using the variable separable method

Q: solve the given differential equation by seperation oF values. dy y xy+4y-* -9 dx xy-Sy tx-5

A:

Q: Solve the given differential equation by separation of variables. dy xV1- y2 %3D xp

A:

Q: Solve the given differential equation (x³ + y³)dx = xy²dy.

A: Differential equation represents the relation between variable and it's derivative. Solution of…

Q: Solve the given differential equation by separation of variables. dy - ху + 4y — х - 4 xp ху — 5у +…

A:

Q: Solve the exact differential equation: (a?y3 - 1 dr+y?dy 0 1+ 9x2

A:

Q: solve the given differential equation. 1. y′=x2y

A: we have been given the differential equation  y'=x2ydydx=x2y             (as y'=dydx) using the…

Q: Solve the given differential equation (2x-y +2)dx + (6x -3y +1)dy = 0

A: Given:                              (2x-y +2)dx + (6x -3y +1)dy = 0   Solution:…

Q: Solve the given differential equation. (y² + 5) dx = y sec²(x) dy

A: For the given differential Equation (y2+5)dx=ysec2(x)dy is  y=cex+cosxsinx-5 , y=-cex+cosxsinx-5

Q: solve the differential equation dy/dx=(4x+y+1)^2

A:

Q: Solve the given differential equation by separation of variables: = 5y dz Oy = cr5 ) y = ¿xª +c Oy =…

A:

Q: c) Solve the differential equation ydx = (ye" - 2x)dy.

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Q: Solve the given differential equation y" + 3y" + 3y + y = 0

A:

Q: Solve the linear differential equation dy y 2x2 dx

A: This ODE can be solved as follows:

Q: x²y" – 2y = 0

A:

Q: Solve the differential equation: dy + 2xy = y da

A:

Q: solve the differential equation : y"+k?y=0

A: We will be solving y''+k2y=0. So,

Q: Solve the given differential equation dy = e-Y. dx

A:

Q: Solve the linear differential equation dy y 2x2 - dx

A: Given differential equation is dydx - yx = 2x2

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.