The degree of y' =2x +3 .A 2 .B 3 2 .C .D 3

Q: 4. (у- 2ку + 6x) dx - (x?- 2ху + 2) dy -0

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Q: General solution of differantial eq.? y'' + y = tan(t)

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Q: (ve-2x + y²) dx - e-2x dy = 0 6. (ye

A: We need to identify the given first order differential equation as homogeneous, Bernoulli, linear…

Q: 1. у%3D х3 — 2x2 + 3х — 5 y = 3 — 2х2 + 3х — 5 dy — Зx2 — 4х + 3 dx

A: Given: y=x3-2x2+3x-5

Q: 1.S (3x5 – 2x – 5x – 3) dx 2.5 (y? – 1) (3+2y) dy 3.S V + 5VX³ dx

A: Dear student. Since you have posted many sub-parts, in our policy, i have answering the first…

Q: .3 Cos x + cos x dx Vsin a 3,

A: Given…

Q: With the help of Weingarten equation show that H[ñ ñ2 ] = FN – GM %3D

A: Given: To show the given statement as follows, The given  H    n→  n2→  r2  →  = FN - GM.

Q: 2. 3x(xy – 2)dx + (x³ + 2y)dy = 0

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Q: Homogenous (2x²y + y³)dx + (xy?. 2 – 2x³)dy = 0 -

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Q: 3. General solution of x dy = (2xe* – y + 6x²) dx

A: The given differential equation,     x dy=2xex-y+6x2dx

Q: y' %3Dх (1 — у?) 2 2ху — 10у —х+5g- 0 ху +5у + 2х + 10 2х + 3 -dx + dy = у — 6

A: given differential equations are first order variable separable differential equation. We will first…

Q: ) ور شم( موم 2 4-x 2 2 4-x 2 x++y¯+z° e - dz dy dx -2

A: To evaluate the below integral. ∫−22∫04−x2∫04−x2−y2e−x2+y2+z23/2dz dy dx

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: Solve using method of variation of parameters. 6. y" + 3y' + 2y sin(e*)

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Q: Evaluate the integrals

A: Given I=∫01∫03-3x∫03-3x-y1dzdydx

Q: dy ху + 2у - х-2 ху — 3у+x-3 dx

A: We will solve the problem

Q: (a) (Ex) ((Ax --> Bd) --> Ky) (b) (Ex) ~ (Dx v Cy) (c) -(x) (Dy --> (Hx v ~Ga))

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Q: 7,9,-4) y dx +x dy +3 dz = (5,4,1)

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Q: = 6 + 3t, y = −8t;  dy dx

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Q: dz/dx&dz/dx at the point (1,1,1) Find the value of if the equationxy + z³x - 2yz = 0.

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Q: d’y - 2 y = 5x' + In(x²). dx

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Q: 2.x 2- L* (6- 22 - 3y) de dy 6 — 2 — Зу) dx dy

A: The integral is ∫03∫02-2x36-2x-3ydx dy. To evaluate the integral, first evaluate the integral with…

Q: 2x dx by taking n = 4 1+ x Use trapezoidal Rule to evaluate

A: trapezoidal rule

Q: 2(х + у)dx — x(х + 2у — 2)dy %3 0? -

A:

Q: (3sin y– 5x)dx+2x² cot ydy = 0 3.

A: Given: 3siny-5xdx+2x2cotydy=0

Q: Find a linear equation that has the same solution set as th e given equation (possibly with some…

A: We need to find a linear equation that has the same solution set as the given equation.

Q: (3-y)dx + (y-2=) dy = 0, y(-1) = 2. ry2

A: Given: 3-yx2dx+y-2xxy2dy=0, y(-1)=2

Q: 1- 2r (1 + y')dx - y (1 + 2x)dy =

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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: 5/xy dy -2, х, у» 0 dx y =

A: See the details solution in below

Q: Intergrate:

A: To evaluate the integral.

Q: Solve for particular solution. (2x-6y+4)dx + (x-2y-3)dy = 0 ; when x = 1, y = 1

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Q: 10-4z .5-2x-y 6z2 dz dy dx

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Q: dy 1.- dx ах — by bx — су

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Q: 2x dx by taking n = 4. 1+x Use trapezoidal Rule to evaluate

A: on solving this we get

Q: 3. fz √z dz 4. (2x² 3x + 5) dx -

A: 3. ∫zzdz4. ∫2x2-3x+5dx

Q: 1. (2x -х-у)dx- хdy - 0; y(1) -о

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

Q: 3. (х+1)dy %3D (2хe* - ху- 2у)dx

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Q: dy 2 = 3, ,3 X'y' - xy dx

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Q: Solve the LDE of dy/dx = [1/(1+x3)] – [3x2/(1 + x^3)]y

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Q: 3z (sec-(-3z?))³ 2|–3z*|-/9zª–1 If y= sec-1 (-3x²), then dy dz

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

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Q: 3) Find d²y/dx² at the point (1, 1), if x6 + y6 = 2.

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Q: 7. dx * = + 2 dy Lal

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

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Q: 7 5-y y dx dy 3y

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Q: 9-y dy 5. S y

A: We will use trigonometric substitution.

Q: Vaz x² S. (2) dy dx

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Q: 3.2.2 Test for exactness then solve. y(2xy2 − 3)dx

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Q: Determine dy/dx for the equation 5x3+7xy- 3y5 = 9 .

A: To find the derivative (d y / d x).