(a) Put the following equation in standard form dy + 3yx? = e* dx x > 0 %3D (b) Find the general solution of the differential equation dy x>0 - dx x3

Q: Find the particular solution of the differential equation dy 6x° e -x* : y(0) = 3 dx

A: We need to integrate both sides for particular solution

Q: Find the general solution of the differential equation dy/dx = 2.

A: dy/dx = 2 Integrate both sides w.r.t x to get: y = 2x + C where C is the constant of integration

Q: Given a differential equation as d²y x2 dx² +4y=0. dx By using substitution of x = e' and t = ln…

A:

Q: Find the general solution for the given differential equation. dy dx

A: To find the general solution of the given differential equation.

Q: Calculate the value(s) of C for which y=x'-2C is a solution to the differential equation dy -3y-54 =…

A: We have to find the value of C

Q: Find the general solution of the differential equation.

A: The general solution of a differential equation is an expression of y in terms of x. To find the…

Q: 2. Find the general solution of the differential equation: dy dy -5 + 6y = e* dx? dx

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Q: 1. Find the general solution of the differential equation: d°y d'y dy , dy - - dx6 dæ3 dx2

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Q: Find the general solution of the given higher-order differential equation. d4y/dx4 + y = 0

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Q: Find a general solution of the differential equation dy/dx = y2. 29.

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Q: Find the general solution of the given differential equation. x dy/dx + 3y = x3 − x

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Q: Find the general solution of the given higher-order differential equation. (d4y/dx4) + y = 0

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Q: Find the general solution of the given higher-order differential equation. у" — бу" — 7y'%—D 0 y(x)…

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Q: 2. Find the particular solution to the differential equation dy 2y? dx cosec (x) if the point…

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Q: Find the general solution for differential equation.

A: Given differential equation is xdydx+2xy-x2=0. To find the general solution of the given…

Q: Find the general solution of the given differential equation. d'y 4 dx dy dy 5- = 0 - dx dx

A: Given differential equation is d3ydx3−4d2ydx2−5dydx=0 We have to find the general solution of the…

Q: The general solution of the differential equation xy^2 dy – dx = 0 is -

A: Firstly separate the variables and after that integrate on both sides.

Q: 3. Solve the given differential equation xy dy - (x2 +y)dx

A: The given differential equation is  xydy - (x2 +y2)dx = 0 (x2 +y2) dx - xydy=0

Q: 2. 2 ydx + x(x² In y-1)dy=0

A: Solution is given below:

Q: 1. Find the general solution of the differential equation cos x 1. dy 2 y2-4 dx 2y

A: Solve differential equation by seperation of variable:-

Q: In the process of solving the differential equation dy xy dx using the separable method, we get:

A: Consider the following differential equation: dydx=xy1ydy=xdx Integrate the above equation:…

Q: Find the general solution of the differential equation.                                  dy/dx = (1…

A:

Q: Solve the Bernoulli differential equation dy 2 y3 +-y dx X x3

A:

Q: 1. (а) Put the following equation in standard form dy x3. + 3yx? = e* x >0 dx (b) Find the general…

A: To write the given equation in standard form and to find the general solution to the given…

Q: What is the general solution to the differential equation (x+y-1)dx+(3x+4y-2)dy=0

A: Differential can be solved by different method  By variable separable By homogenous method  By…

Q: Solve the differential equation dy xy y(0) = -3. dx V1+ x? There is no need to isolate y.

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Q: Find the general solution of the given differential equation. + 40y = 8 dx dy

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Q: Solve the non-homogenous differential equation below dy 2y + x - 3 dx y + 2x – 3

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Q: Find the general solution of the given higher-order differential equation. ²y - 32y = 0 dx² X(X) 11…

A: Find the general solution of the given higher-order differential equation.

Q: Find the general solution of the separable differential equation dy dxy (2x + 3) e3y

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Q: Find the general solution to the differential equation dy x3 dx x² – 1

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Q: Solve the differential equation: dy/dx=-8y with the initial condition of y(0) =3

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Q: 1. Find the general solution of the differential equation: dy, dy + dx3 dºy dy = 0 dx6 dr5 dx?

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Q: Solve the differential equation dy 1 dx 3y? by the method of separating the variables.

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Q: Find the general solution of the differential equation. dy/ dx= x2(√x − 3)

A: ∫xndx=xn+1n+1+C

Q: Find the general solution of the differential equation dy/dx = x/(x2 + 2)

A: Given: dydx=xx2+2 for finding solution of given differential equation, we use variable separable…

Q: - find the solution of differential equation dy 1+x e* dx

A: I have used method of integrating factorr

Q: What is the general solution to the differential equation (x+y-1)dx+(2x+2y+1)dy=0

A: Given:              x+y-1dx+2x+2y+1dy=0 Rewrite as:             2x+2y+1dy=-x+y-1dxdydx=-x+y-12x+2y+1…

Q: Find the general solution of the given second-order differential equation. Зу" + 2y' + у %3D0 y(x) :…

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Q: Find the general solution of the first-order linear differential equation. dy 2y dx x > 0 y =

A:

Q: The solution of the differential equation dy x+x+2xy %3D dx x2+1

A:

Q: 3 Find the particular solution of the differential equation dy (x+2)= y+2 dx y(0) = 1

A: To Determine :-  The particular solution of the differential equation x+2 dydx = y + 2            y0…

Q: Find the general solution of the given differential equation: dy = x²y %3D dx

A: Solving

Q: The solution of the differential equation dy dx 5x + y is

A:

Q: dy 5. x - y(In xy – 1) = 0 dx -

A: We have to solve given problem:

Q: (1 + In xy) dx + (1 + x/y) dy = O

A: The given exact differential equation is…

Q: Question 2 Determine the solution of the second-order differential equation: d'y dy dx2 -7-+12y=e-10…

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Q: Solve the differential equation of dy/dx + 1/3 y = e^x y⁴

A: Divide both sides of the given differential equation by y4 to obtain the right hand side y free.…

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.