y' = - 2xy

Q: Find general solutions of the differential equation     x(x+y)y'+y(3x+y)=0

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Q: y" + 9y' + 7y = e-2t ,t > 0[

A: Using method of Laplace Transform.

Q: What function satisfies the differential equation y - y' = 0?

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Q: Find the general solution of the differential equation y′ = √x y

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Q: Solve the differential equation by variation of parameters. -t y" + 2y' + y = et In(t) y(t) =

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Q: Solve the differential equation by variation of parameters. y" + 2y + y = et In(t) y(t)

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Q: Solve the differential equation by variation of parameters. y" + 2y' + y = et In(t) y(t) =

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Q: y"+2y'+y= e "Ina -

A: Consider y''+2y'+y=e-x ln xConsider the homogenous equation:y''+2y'+y=0Let y=eλx be the…

Q: Verify that the function y = 2x - 6x + 10 satisfies the differential equation -y"-xy"-2y' = -24x.…

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Q: Solve the differential equation by variation of parameters. 1 y" + 3y' + 2y 5 + ex y(x) =

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Q: Find the particular solution to the differential equation. 4y2 dx = 3x2 dy when x = 4, y = -1 %3D

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Q: Find the differential equation that has y = C1 + C2x as its general solution.

A: To find the original differential equation we  have to eleminate the arbitrary constants by…

Q: Obtain the solution of the differential equation y′ = (x + y)^2

A: Given differential equation is: dydx=(x+y)2                       (1) Let us assume (x+y)=t…

Q: Obtain the differential equation y = x^2 +Ae^2x +Be^3x

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Q: Find the differential equation whose general solution is y = C1x + C2ex. %3D

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Q: a. y = C,e=x + Cze-2x + x

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Q: Solve using linear differential equation (y+1)dx+(4x-y)dy=0, when x=4 and y=4

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Q: Find the general solution of the differential z-y+3 equation y' I-y

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Q: Find a differential equation whose general solution is y = c₁et + c₂e-4t . = 0

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Q: Solve the differential equation by variation of parameters. y" + 3y + 2y = 8 1

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Q: y(4x + y) dx - 2(x² - y) dy = 0

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Q: y = Ax² + Be*

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Q: Find general solutions of the differential equation    (x+2y)y'=y

A: Given differential equation is Convert it in linear differential equation by simplifying. This is…

Q: The differential equation (xy+ x) dx = (x<y² – x²+y- 1) can be rewritten as

A: Consider the differential equation  xy+xdx=x2y2−x2+y2−1dy

Q: find the differential equation of y'' + 5y' + 6y = 0 when y (0) = -1, y' (1) = 3

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Q: Find the general solution of the differential equation. y′ + √x y = 9√x

A: To find the general solution of the differential equation y'+xy=9x

Q: For the given non exact differential equation, determine the integrating factor. (x2 + 2xy - y2) dx…

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Q: Find a differential equation whose general solution is 9t = C₁e⁹t + c₂e-5t. y = = 0

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Q: Find the general solution of the differential equation xy′ = y

A: Since, we have to find the general solution of the differential equation given below:-xy'=y-(i)

Q: ylv – y" = 4x + 2xe-*

A: the

Q: Match the differential equation with its solution. y' - 4x'y = x3 %3D

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Q: Find the particular solution of the differential equation when x = 2, y = r. %3D y y' = sec y

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Q: Solve the differential equation by variation of parameters. y" + 2y + y = e-tIn(t) y(t)

A: Given the differential equation is y''+2y'+y = e-t lnt

Q: Solve the differential equation by variation of parameters. 9x y" - 9y = %3D 3x e y(x) =

A: The given differential equation is y"-9y=9xe3x.

Q: Find the solution of the differential equation y'+ y = x?

A: Please refer to the image below

Q: Solve the differential equation by variation of parameters. 1 y" y² + 3y + 2y = 2 + ex

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Q: Solve the differential equation by variation of parameters. y" + 3y + 2y = = 1 2 + ex

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Q: Determine an appropriate substitution and then solve the differential equation. xy' = y In(xy)

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Q: Determine the differential equation whose general equation is 1. y = Ce-2x + C,e3x 2. y = Ce* +…

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Q: 2xydx – (y² – x²)dy = 0 ; x= 4, y = 0

A: Note the following exact differential equation : x dy+y dx=dxy 2xy dx+x2dy=dx2y .

Q: Find a differential equation whose general solution is -4t y = cjet + cze¬4.

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Q: Verify that y = (x³ – x) In cx satisfies the differential equation (x³ – x)y' – (3x² – 1)y = x5 –…

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Q: Solve the differential equation using the method of undetermined coefficients. y" – 2y' + 2y = x +…

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Q: Solve the differential equation by undetermined coefficients: y" + y – 6y = 2.x.

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Q: Use a substitution to solve the nonlinear differential equation: (y + 1)y" = (y ')²

A: Let y' = t Then , y''=dtdy  to find the value of y, integrate y' =t⇒∫dy =∫t. dt⇒      y =t22  So the…

Q: с. у -у%3х y = x

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

Q: b. y = C, + Cze3*

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Q: Find a differential equation whose general solution is 6t y = c₁et + c₂e -3t = 0

A: We find a differential equation whose general solution is y=c1e6t+c2e-3t.

Q: Solve the differential equation by variation of parameters. y" + 2y + y = et In(t) y(t) =

A: Given : The given differential equation is y''+2y'+y=e-tln(t). To find: The solution y(t) for the…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.