xy' – y – 5x* – 3x² + 2x = 0 when x = 1 and y = 2

Q: y(x²-1)dx + (x³+8y-3x)dy =0  when x=0, y=1

A: Given: 3y2(x2-1)dx+(x3+8y-3x)dy=0initial condition is x=0,y=1

Q: (2x + 3y - 1) dx - 4 ( x + 1) dy = 0

A: Explained below

Q: y (8x - 9y) dx + 2x (x -3y) dy = 0 where x = 3 and y = 7

A:

Q: dx dt -1 -3 [:] 2 with x(0) 4 Give your solution in real form.

A:

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: (x² + 2xy - 4y²)dx – (x2 - 8xy - 4y²)dy = 0 when x = 1; y = 1

A:

Q: Solve for separable equation xy +5y + 2x + 10 2xy - 10y -x +5 6. 2x + 3 -dy = 0 y - 6

A: The given differential equation is: xy+5y+2x+102x+3dx+2xy-10y-x+5y-6dy=0 To solve the differential…

Q: Find dy dx 2 for x²exy = 5 WA/

A:

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t and x = sec-1t

A: To find: The value of dydx in terms of x and y. Given information: y=csct,x=sec-1t

Q: . Form the differential of the system of circles touching the y-axis at the origin.

A: The solution is given as

Q: 2ydx-(1-x^2)dy=(x^2-1)dx when x=0 and y=-1

A:

Q: Only I method. Except Exact DE (x+2y-1)dx+(2x+4y-3)dy oo

A: First we campare the given differential equation Mdx+Ndy= 0 and then solve it.

Q: y 2sin x-cos 2.x for 0° sxs360

A: Consider the function, y=2sinx-cos2x Differentiate with respect of x,…

Q: /2x- xy dydx = 0,

A:

Q: 2x+2 dx. 5. x2-2x+1 dy 6. 5. if y = (1+ x²)etan-1x

A:

Q: -2x y" + (e by = 0 (e-* = z) -

A:

Q: find dy. y = sec (x2 - 1)

A: Given: y=secx2-1 we know that ddxsecx=secxtanx

Q: 2x(y + 1) dx – ydy = 0 when x = 0, y = -2 %3D -

A: Here differential equation is given as 2xy+1dx-ydy=0or2xy+1dx=ydy⇒2xdx=ydyy+1⇒2xdx=dy-dyy+1

Q: Use variation of parameters to find the general solution: x^2y''+xy'-y = ln (x)

A:

Q: d’y - 2 y = 5x' + In(x²). dx

A:

Q: 2y (x+y+2) dx + (y²-x²-4x-1)dy = 0 when x=2, y= 3 |

A:

Q: x'dx √√x(1-x)

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Q: By using chain rule Find dy/dx iff- u=-1, x=-1

A:

Q: Q2. Find the second order partial derivative of x² - y² + 2xz - xy + yz.

A:

Q: Find all the second partial derivatives forf (x, y) = x³y5 + 2x*y.

A: All the solutions are given below.

Q: find the first partial derivative  f(x,y) = squareroot (2x+y^2)

A:

Q: 10. x = Vt-2, d²y y =t2-3' dx2

A: The given question is taken from the derivative and we have to find the derivative of the parametric…

Q: Find the partial derivative. = (a² + 4x – 2y)° - dz II

A:

Q: Differentiate the function y = 6 + x using the Chain Rule. dy %3D

A: Given, the function is                              We have to differentiate this function using…

Q: Ssin^3 (2/3 x) cos^4 (2/3 x) dx

A:

Q: d²y dy + 3x+y = 4sin (In(x)) dx²

A: Given Euler differential equation is: x2y''+3xy'+y=4sin(ln(x)) Let us take x=ez Replace:…

Q: Find the solution of the DE using reduction Order (D2 + 4)y = sinx

A:

Q: 14-2x 1. ! ] dydx 0 2 2. dxdy 0 y 11-r 3. dycx o 1-x 4. [[ dydx 0 0

A: Answer 1: changing dy dx to dx dy; limits of integration: 0 ≤ x ≤  [2 - (y/2)] 2 ≤ y ≤ 4

Q: By differentiating x² – y² = 1 implicitly, show that d²y | dx² ||

A:

Q: Find dy when X= 4 and dx = 0.2. y 3x-4x + 2x+ 3x -7 y%3Dx

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Q: y = (2x3- 8x )4 Find dy/dx when x = - 2

A: Given function is Differentiating with respect to x by using chain rule o differentiation, we get…

Q: (x³ + y³) dx - 3xy² dy = 0; when x = 1, y = -1

A: The given differential equation is in the form  Mdx + Ndy = 0 x3+y3dx-3xy2dy=0 where M = x3+y3 and N…

Q: (2x+ 3y) dx + (3x-y+5) dy

A:

Q: Find the four second partial derivatives. z = 6x2 + y5 a2z дхду дудх ду?

A: We will find all the asked second order partial derivatives as following.

Q: sin(3z+z²) Find y' for y = (6 – 2*)3

A:

Q: dy_2y-x+5 dx 2x- y-4

A: Find the solution of the ordinary differential equationdydx=2y-x+52x-y-4

Q: Find dy/dx of  1. y=x3 (2x2 -1)

A: Given, y = x3(2x2 -1) Multiplying the x3  with (2x2 - 1)  So, y = 2x5 - x3

Q: (6x²-y+3) dx +(3y²-x-2) dy

A:

Q: Find the partial derivative. 2 = (r² + 5z – 6y)“ az ||

A: The given function is: z=x2+5x-6y4

Q: .x(3xy-4y3 + 6)dx + (x³ - 6x²y2 - 1)dy = 0, when x = 2, y = 0

A:

Q: 9) (x- y°-Ay-1) dx t 2x (x4 y +2)dy =o

A: As we know that the differential equation Mdx+Ndy=0 is exact, If ∂M∂y=∂N∂x. The solution is:…