y = Vx3 – x y = x - Vx - 1

Q: Find dy/dx: 4x²-3 y = Vx2–1

A: The given function is, y=4x2-3x2-1 To find the expression for dydxwe need to use to division rule of…

Q: - f(x, y) = Vx5 + y5. Find f-(0, 0).

A: Given that fx,y=x5+y55.It is required to find fx0,0.

Q: (3x² + y² + 4) dx + (x² – 2x y) dy = 0 %3D

A: 3x2+y2+4dx+x2-2xydy=0Let y be the dependent variable. Divide by…

Q: Find y': y=- Vx* + 4

A:

Q: Use variation of parameters. a. (D^2 − 1)y = e^x + 1

A: Given equation is (D2-1)y=ex+1

Q: xydx + (y/x² + y² – x²)dy = 0

A:

Q: f Gx,y) x+ 3 XY %3D

A: We have to check

Q: rx dydx Vx2+y2 0.

A: We solve this double integration problem by substitution method as given below in solution

Q: 1. y= (x +1) Vx² + 2x + 1

A:

Q: (6x + y2) dx + y(2x - 3y) dy = 0. evaluate

A: The given differential equation is                                    (6x+y2)dx+y(2x-3y)=0

Q: (y + Jx² + y² )dx – x dy = 0 ; when x = v3,y = 1 7.

A: The given problem is to solve the linear differential equation with given initial conditions. We…

Q: x² dy = x*y% + xy - 3

A: This is reccati differential equations, but this can be solved in simple way.

Q: y = (x+1)Vx +3

A:

Q: dy * + 2(t + 1)y² = 0, _y(0) = - ip 1/8

A:

Q: y(2x²-xy+y²)dx-x²(2x-y)dy = 0, when x(1/2) = 0

A: Given: Differential equation is homogeneousPut x=vy⇒v=xyDifferentiate both…

Q: "+y=と(t - kT), y(0) = 0, / (0) = 1. k=1

A:

Q: Зx t2-1 dt dx '2x t2+1 d

A:

Q: 1) y = Vx -1

A: According to our guidelines we are suppose to do only one question . Kindly repost other question as…

Q: Find ax dy x-2–1 given y = 2x3

A:

Q: 3. y = 1 √x Calculate y'. 1 V3

A:

Q: -2 (x² - y²)²] Evaluate: S₁ S² P₁² dx dy x+y

A: Let's evaluate given double integral.

Q: アT x=2 y=2 7+3x-6y dy dx x0 y=1

A:

Q: Find dx² given d²y given X² – y³ = 5.

A: Given that: x2-y3=5

Q: y(x² – y² + 1)dx – x(x²-y² – 1)dy = 0

A: Exact differential equation

Q: 2) 2x2 csck) dy d X M) y'= Xe'Vx-2

A:

Q: F(x) = 9t dt

A: given: Fx=∫0x29t dt Fx=∫0x29t dt=9∫0x2t dt=9t1+11+10x2=9t220x2=92t20x2=92x22-02=92x4-0=92x4

Q: Evaluate VA-x2 4-x2-y2 (x² + y²) dz dy dx. -V4-x2 0.

A:

Q: dy (x³ + 1)(x² – 2x-1+ 1) of y = dx x² + 3

A: y=(x3+1)(x2-2x-1+1)x2+3

Q: y = Vx – 2, y = x – 2 %3D

A:

Q: x = t – 1 * (D) : y = 2t + 3 x = - t'+ 1 (D') : y = t' - 2

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

Q: y(4x+y)dx-2(x2-y)dy = 0  when x = 1 , y= 1

A:

Q: find dy. y = 2x/1 + x2

A: The given function is y=2x1+x2

Q: dy 2x – y 21 dx x - 2y

A: The given differential equation isdydx=2x-yx-2y

Q: 2 X; glo)=0; y(0)= | 2. t.

A: To find- Solve the given differential equation y'' + y' - 2y = 2x ; y0 = 0 ; y'0 = 1

Q: dx xy dy x² + y² Ans. y² = 2x²ln (

A:

Q: dy 1+y2 x2 3. dx +y²

A: Given: dydx=x21+y2 For finding solution of given differential equation, we use variable separable…

Q: using variation of parameters: - 2x + x = e t (et 1 1)2

A:

Q: x/1-y2 B, dx %3D 1+x²

A: dydx=x1-y21+x2

Q: 2x2 f' (æ) = If f(x) = V 1+t° dt, then

A: To find the derivative of integral apply the follow rule

Q: Find Vy where = (x² + y² + z²) e¯¯ √√√x² + y² + z ²

A: Given :ψ=x2+y2+z2e-x2+y2+z2

Q: y(4x+y)dx-2(x^2-y)dy=0

A:

Q: Find of y' (y-x)° = y² – x² dx

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Find dy/dx: 4x²-3 а) у %3D Vx2-1 b) y = x² (x – 1)³

A: Given- a) y=4x2-3x2-1             b)y=x2x-13 To find- dydx

Q: = 0 for F = yz²î +xyj + yzk

A:

Q: (x¹+y¹) dx - xy³ dy = 0 [Answer: y = 4x¹logx + Cx¹]

A: This question is based on Homogeneous differential equation.

Q: d²y Find dy 34 y3 %3D こX+

A: Answer

Q: V1-(x-1)² x + y dy dx x² + y² 2 0. 0.

A: Introduction: The process of determining the area of the region under the curve is known as…