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

Q: b. f(x)dx

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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 (x + y)² dy = a

A: Topic- Differential Equation

Q: 1 с) у- d) y= x 2** e*

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Q: * x' V5 -x°dx

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Q: [xsechtx'dx

A: Topic:- integration

Q: e a) y"+ by 19y x² + 1

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

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Q: (1–3cot.x)² dx cscx

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Q: y = [e2* + (x + In x)³1* %3D

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Q: carctan3/2 3 sec x y dy dx

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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: e*y' = x – 2y

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Q: Get the solution: x^2 dy/dx - y^2 = 2xy

A: Get the solution: x^2 dy/dx - y^2 = 2xy

Q: dx 2. du

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Q: 3 y = (₁ ² +1) ² Gi Find 13y dx²

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Q: Solve the given by simple substitution (2x + y)² dx - 2dy = 0

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Q: t Sintcost de

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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: O Find (a) |VT-x)/x dx, (c) (4-x*y² dx. Ans, ía) 1/60, (/) x/2. (c) 31

A:

Q: Solve: dy dr = y +e*y?

A: The given differential equation is dydx=y+exy2. Rewrite the differential equation as,…

Q: dy et-y dx 2.

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

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

A:

Q: -3x +e xー2) dx

A: Simple integration problem....

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

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Q: y"+ y't 5y-

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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: Solve the following Clairaut equation   xy'-y=e^(y')

A: We will start by differentiation the given equation to get simplified ode

Q: dx х V1-4 In2х

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Q: dy

A: Use the method of substitution and solve the integral.

Q: Solve the D.E Seczx %3D

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Q: So SE 1 + y³ dydx =?

A: To find:-

Q: Solve t-r sec'y= 2g tan y,

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Q: x \dx xV 3 –x?

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

Q: if x3 + y3 =65, find the value of d2y/dx2 at the point (4,1)

A: Given that,    x3+y3=65

Q: Find dy for the following equation. y = 3x/12-x

A: y=3x12-x3 We need to calculate, dy=____dx

Q: Se"dy 3.

A: We have to solve

Q: Solve the following equation. | (2t – 6) dt = 0

A: Recall the rule of integration: Integral of xndx = xn+1

Q: Solve the D.E (X+1) =x(y'い) dメ

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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 (1+) d x = (b an y -x) dy

A:

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

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.