В. NON-HOMOGENEOUS HIGHER ORDERED LDE 1. (D3 + 5D² + 3D - 9)y = 64x²e-3x 2. (D³ + 13D - 34)y = 25x2 + 100e-*cos4x

Q: Obtain the solution using Integrating Factors Found by Inspection y(x3y3 + 2x2 − y)dx + x3 (xy3 −…

A:

Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

A:

Q: 2 dydx + f(x, y)dydx

A:

Q: If y = (2x)sin (4z) , then dy sin(4æ) · (2sin(4z) esin(4z) In(x)) %3D dx X synta

A:

Q: 29, + 16y=0 geoJ = 2, go)= -2 2. 31, dy dy -54 =0 dt

A:

Q: 18y sin3 9y2. 10) +3 cos V9y2 + 3 dy + 3 cos

A: See the attachment

Q: Ssin(2x)dx = cos(2x) + C cos(2x) 2cos(2x) cos(2x) + C O 2 cos(2x)+ C -

A:

Q: dx ylnx- dy y + 1₂ X 2

A: given :ylnxdxdy=y+1x2

Q: z = sin(6x) sin(5y) az az dy II

A:

Q: 5 Find xy dydx.

A:

Q: 1. S(2cos4y – 1)i - sin4ydy

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Find the general solution of y'= sin²xcosy.

A:

Q: 2. [2x*tan y – ysin (2) – 1] dx + [xsin (2) + x*sec*y] dy =

A:

Q: 」enr一2) dz csc (4r – z) dz dz dz 17. 2 V1 – sen 2z V1 – cos (4- – 2z) In | csc (4- – z) – cot (†7 –…

A: Integrate as general

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

A:

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

A:

Q: dy -y2+1,ysCJse Cantial cokditian.

A:

Q: integrate dy/(sb - smy-bny-nmy^2

A: SOLUTION-

Q: Jz{sinh³ 4z*)'^ ² - dz 1/4 cosh³ 4z'

A:

Q: (3) Integrate using an appropriate substitution 2e- -d.xc e + 3 x-

A:

Q: (cos 2y – 3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0

A: We will find out the required solution.

Q: 3. f(x,y) tanx - sec²x - cosy

A:

Q: Show that: 2 2 4: +2} | sin 2y x=1 y=vx TOX dydx = 2y dydx+ _3 x=2_y=vX

A:

Q: S csc“(3y)dy

A:

Q: 13. Equation from Exercise 1; y(0) = 1, y(-2) = -1, y(0) = 3, y(0) = 2. %3D

A:

Q: y" + 4y = 2 sin(6x)+ 6x²e¬3z + 5x,

A:

Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

A:

Q: Obtain the general solution using variation of parameter. (D² + 1)y= cotx

A:

Q: Integrate  zex^2 + y^2  over the cylinder  x2 + y2 ≤ 25, 2 ≤ z ≤ 5.

A: Integrate zex^2 + y^2 over the cylinder x2 + y2 ≤ 25, 2 ≤ z ≤ 5 as follows.Here, x2 + y2 = 25 and…

Q: Intergrate:

A: To evaluate the integral.

Q: (1,2,3) (0,0,0) 4x³y dx + (x²-25) dy-5yzª dz

A: Find the value of function using integrate Compare the given expression with Mdx+Ndy+Pdz to obtain…

Q: 2-if (x - y) (x + y) = 1 prove that d²y + y dx² (2x)² = 1 dx

A: Topic:- application of derivatives    Note:- as per our guideline if more than one question uploaded…

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (8, -3)

A:

Q: obtain the family of solutions [x − y arctan (y/x)]dx + x arctan (y/x) dy = 0

A: The detailed solution is given below Thank you

Q: 2. [ y dy dx carctan3/2 3 secx 3/2

A: Topic  = Integration

Q: 3. Stanh3x dx = Jsinh3x, Ssinh3x_ dx %3D u = cosh3x du = %3D

A:

Q: cos²x sinx dy + (y cos³x − 2)dx = 0

A:

Q: х2 9 dy + sinx - у %3D0 dx

A:

Q: (1+x^3) dy-x^2ydx=0 satisfying the initial condition x=1, y=2

A:

Q: 1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

A:

Q: 3. Find a result by using homogenous for (x³ - 3x²y)dx- (x³ - y³)dy = 0 For Figure 1.

A: We have to find out solutions of differential equations

Q: 5. y" – 2y' + y = 2sinx cosx y'(0) = 0,y(0) = 0 %3D | -

A:

Q: 1-fd dydx R = {0,1} * {2,5} y2 2-S y2 (1–5x)2 dxdy R = {0,1} * {0,2}

A:

Q: f(x csc² 2x - x cos 2x)dx

A: The given integral is ∫xcsc22x-xcos2xdx. The objective is to solve the given integral. Following…

Q: dN1 =rN1 dt (1-*) - aN1 N2(1 – exp[-bN1]), K %3D dN2 = -dN2+ N2e(1 – exp[-bN1]), dt

A:

Q: 1. (sin y — y sin x)dx + (сos x + х сos y — у)dy 3 0 %3D 2. (1— 2x2 — 2х) у' %3 4x3 + 4ху 3. (Зx cos…

A:

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

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

Q: (b) Form the partial equation by eliminating function f from z = f(x?

A:

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (4, -3)

A: To solve the given line integral.