7 1. 2ydx+x²dy = - dx; y = - when x =1 In 2 2

Q: II. Bernoulli's equation: dy 4. dx -2y %3D글x" xy3

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 14 نقطة Q) Find dy/dx of the following * :equation (x² +x)(x' - x +1) y: dy/dx = -3/x^4 O %3D dy/dx…

A: Given y = x2+xx2-x+1x3y = x4-x3+x2+x3-x2+xx3y = x4+xx3y= x+1x2

Q: 5. Find dy/dx (y - x)? = 2x + 4

A: Given: y-x2=2x+4 To find dydx. Solution: Power rule of differentiation states that: ddxxn=nxn-1…

Q: Which one is an integrating factor for the equation y(2x – y+ 1)dx + x(3x – 4y+ 3)dy=0? 9020900 et

A: Given that, y2x-y+1dx+x3x-4y+3dy=0                               ……(1)   The above differential…

Q: Find integrating factor of the equation (x4+y4)dx-xy3dy=0

A: The given equation can be rewritten as   xy3dydx=x4+y4    ∴y3dydx-y4x=x3     Let y4=t…

Q: Solve the equation dy 2 dx with the initial condition y (1) = 1. 2/3

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Q: 1. S(7x³ + 4x²)dx e*dx 2. J itez* 1+e2x 3. S(V1 – cos x)dx

A: We will these indefinite integrals as

Q: Find the general solution of

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Q: Solve dy/dx =( y+x-2) /(y-x-4) Equation s reducible to homogenous form

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Q: (1)Find the general solution for (- x) dx – (-y) dy = 0

A: Here, the given differential equation is  (2xy3-x)dx-(3x2y4-y)dy=0

Q: dx ex -1

A: Let ex=t ⇒exdx=dt    dx=dtex          =dtt

Q: 2. If y= 2u'and dy when x-1. dx determine 2x -1

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Q: Find dy dx dz 2 9=(z-3 Inax) a = constant

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Q: у (буз — х — 1) dx + 2x dy — 0 || -

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Q: Obtain the general solution to the equation. dy 1. y + 2x + 1 dx

A: Given that: dydx=yx+2x+1

Q: 1. ſx² e*³ Sx² e**dx 2. cos'xsinxdx sin3xsin 2x dx 3.

A:

Q: 5. Find the particular solution (IVP) for the DE below: a) dx +2 =8x when x = 2, y = 6 b) 3y2 = 2x +…

A: Use variable separable method

Q: 4. Using homogenous D.E approach, solve (x³ – 3xy?)dx = (y3 – 3x²y)dy.

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Q: 2.x²y+ 3xy? = 2x + 55

A: We will find the value of dy/dx and the equation of the tangent line at point (5,1) in the following…

Q: 4. Bernoulli's Equation 3dy – 4xy dx = 3x²y*e=2x² dx Зdу — 4xу dx

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Q: 5) SOLVE dy 2 y (1) == (ive) dx 2

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Q: 4. (x³ + 3x – 1) dx 2 5. 4x x2 6. SIy + 1) – (y? - 1)]dy

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Q: 6. J 4 x4-1 -dx

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Q: pom ais Question dty Find of y = 6 cos (x). dx 54 Provide your answer below: -口 dx * Previous Aa

A: topic - derivative of trigonometric functions

Q: 1. Solve the equation 3(y+1)dx-(x+y+3)dy =0.

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Q: dx √ex +1 S=

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Q: (1) Find the general solution for (+) dx + (--) dy = 0 %3D

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Q: 2. S dx exte-x 3. fx sec² x dx 4. esinx cos x dx

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Q: 3 7x + 6x - 5x dy find dx - Example 28. If y = 4

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Q: 30. Find the solution of exe dx-e-2Y dy = 0 %3D

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Q: 11. Put the following equation in separated form, do not integrate. dy с. = sec (y)e*-y(1 + x) dx

A: A detailed solution is given below.

Q: 5. S , dz dy dx 2 c3

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Q: (5x )cos( - Jax + S, (5x – 15)cos( 1.5 a 1.5 1.5 dx

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Q: Find the general solution of the equation: G + 6x) dx + (In x – 2) dy = 0 (x > 0) -

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Q: dy dy = xy + 3x – 3x dx dx

A: The given differential equation is: dydx-x2dydx=xy+3x-3x3Therefore:dydx=xy+3x1-x21-x2

Q: 2 What is wrong with the equation dx =

A: Use the formula ∫xndx=xn+1n+1, to evaluate the indefinite integral ∫4x3dx.…

Q: Find the solution to the equation 2ydx – 3xy'dx – xdy = 0 using integrating factor by inspection.

A: The solution are next step

Q: dx 3. S ex+ e-*

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Q: (ve* +y)dx+(2xye* +1)dy = 0

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Q: 1. (2x -х-у)dx- хdy - 0; y(1) -о

A: Given that: (2x2-x-y)dx-xdy=0; y(1)=0

Q: 4. if x^3+y^3=2 find the value of (d^2y)/(dx^2) at the point (1,1)

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Q: (х — 4у — 3)dx — (х — бу —5)dy — 0 -

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Q: In Prob. 1-38. Find dy/dx.

A: Given; y=e2x+3.

Q: Solve dy/dx−6y=3 subject to y(2)=2

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Q: What integrating factor should be used to find the solution of the equation ydx + (xy + x- 3y) dy =…

A: Given that: ydx+(xy+x-3y)dy=0

Q: Obtain the general solution to the equation. dy 4. x+ 2y = x-3 dx

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Q: 1. Find the general solution of 3 + = y*(2x*) dx

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 12. Find dy/dx (x – 2)(x + 1) 3 X y = (х — 3)4 -

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Q: (b) 6x Cos dx. (Hint: you might need to use integration by parts several times.

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Q: 11. Put the following equation in separated form, do not integrate. dy b. dx ху (x+1)(y+1)

A: