Solve the following D.Es: 1. (x + 1) = x(y² + 1).

Q: dx (V32 + 4)3

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Q: find the seril solution of the equation y``+  4xy = 0  at the neighborhood of the  point  x0 = 0

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Q: Solve the following 2nd order D.E: y'' + 2 y' = x^2-e^x

A: given ,         differential equation,   y''+2y'=x2-ex

Q: Solve (x + y)² dy = a

A: Topic- Differential Equation

Q: 1 с) у- d) y= x 2** e*

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Q: Solve for the following problems using substitution suggested by the equation. (3siny – 5x)dx +…

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Q: Solve the following IVP correctly: x3+y3 dx + 3xy2+y3-2 d'y=O

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Q: y = [e2* + (x + In x)³1* %3D

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Q: Solve the following D-E 3) + y = y³ dx

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Q: Solve the following IVP: (x²y+y +5x2 +5)Y =y2 +y-2; y(1)=2 dy dx

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Q: Find dy for the following equation. y= 3x/4 -x3

A: Given: The function is  y=3x4-x3   To determine: The differential dy for the function y=3x4-x3

Q: .Solve the following D. E y" + y' – 2y = x³ +x

A: y"+y'-2x=x³+x

Q: A. Solve the following DE by using exact equation method: y = x - y,

A: The given differential equation is dydx=x-y ⇒x-ydx-dy=0 ⇒M=x-y and N=-1⇒∂M∂y=-1 and ∂N∂x=0⇒∂M∂y≠∂N∂x…

Q: Solve the DE below: y' – y = 1+ t(e'); y(0) = 2

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Q: Solve the following DE x y" – 4y' = x e"

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Q: Solve the following SLP y" + ly = 0 y(0) = y(1) = 0

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Q: 2. (x+53y)e dydx %3D -1J0

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Q: Identify f(x) to be used in variation of parameters to solve for y, e" y" + y' – 3y = x

A: To find f(x) write equation in form of y" + P y' +Q y = f(x).

Q: Solve the equation dy y + dx ху 3

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Q: Solve the following DE: (2æy + 3z?) da + (2x²y+4y) dy = 0

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Q: 2- Solution of the following function {(dy/dx)-(cotx) y=(csc x)y³ }

A: The differential equation is given as dydx-(cot x)y = (csc x)y31y3dydx-1y2cot x = csc x…

Q: dy et-y dx 2.

A: The given problem is to solve the given differential equation using separation of variables method.

Q: 1. (x + y) dx + (:

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Q: What is the solution for y(t)?

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Q: y =

A: We have to solve

Q: E=メ (x)NIb=R TANGET Nge of EQUATION 12)

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Q: 3 y = (x² +1) ² Find day dx ²

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Q: (D² + 1)y = sec² x csc x X cSC X

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Q: Given: f(x, y) = x³y – y cosh xy Solve for D132

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Q: Find the solution 7. (x + 4y³)dy - ydx = 0

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Q: dx is is equal to: 2x/4-(2x)2

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Q: Solve the following equations: (x² - 4xy - 2y²) dx + (y² + 4xy - 2x²) dy = 0

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Q: Q/ Solve the DEs: 1-a+ykdx+(1+x*)dy = 0

A: 1-(1+y2)dx+(1+x2)dy=0

Q: Solve the D.EXY+Y=1/1/2

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Q: xy dy + (x^2+y^2) dx=0

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Q: Find y = (2x²² -6) ⁹ dy اده

A: We can find the derivative as below.

Q: x \dx xV 3 –x?

A: We need to evaluate the given definite integrals. each part is solve on each steps.

Q: Solve the Fo (lowin) D-E e* y+2 ey =2X 2X

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Q: Solve by making the equation into an exact equation. (2 – x - y) dx + (3 +x + y) dy = 0

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Q: e: √₂² ²₁₂₁ (4x²yz - ²) dz dy dx 4

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Q: Se"dy 3.

A: We have to solve

Q: (1 + x)dy – ydx = 0 %3D

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Q: Solve the following equations: y dy x² + y²-1 x dx 2(x²+y²)+1 + 0

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Q: Q/ Solve the DEs: 1-a+yxdx+(1+x)dy = 0

A: 1-(1+y2)dx+(1+x2)dy=0

Q: Solve the IVP d'y = 4sec 2x tan 2x, y' (0) = 4, y(0) =-1 dx2

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Q: solve the following equation y(2x² – 2xy+ 1)cx + (x– 2y)dy = 0

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Q: 6. (2ху + x) dx + (x2 + у) dy 3 0

A: the given differential equation is: 2xy+xdx+x2+ydy=0 we have to solve the given differential…

Q: Fh(x)= x° – 5xª – 35a³ 35x3

A:

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.