f(z) dz = 4, then 2f(x) – z dz 13 If %3D =

Q: Higher Order L.D.E (D2-2D+10)2y=0

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Q: Is y = e-x + 2xe-* a solution to y" + 2y' + y = 0.

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Q: Find the particular solution of (y + Vx² + y²)dx – xdy; when x = v3, y = 1

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Q: y (z² + yf) dz – a (z² – y²) dy = 0 %3D

A: Use substitution

Q: If y = f(x) is the solution of y' – 3y =-12.e 9z, f(0) =1, then

A:

Q: A. Find the general solution of y" = 12x². dy B. Solve for y F dx - 4 x²-1

A: The given differential equations A) y''=12x2 B) dydx=4x2-1 use the integration formulas,…

Q: determine L−1[F].

A:

Q: S Sz(x² + y³)dxdy, wherein B = {(x, y) E R²; 0 < x² + y² <4}.

A: Double integral

Q: Non Homogeneous: (D2 − 7D + 6)y = 3x2 − 2x + 5

A: Here we have to solve the non-homogeneous differential equations     (D2-7D+6)y = 3x2 - 2x +5 .

Q: y'' - 6y' + 9y = x^-2(e^3x) using Methods of Variation of Parameters

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Q: xy = e2x; y 2х ху — е

A: We will find y' as following.

Q: Find the General Solution: y" - 3y' + 2y =e*

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Q: (D³– 4D°D'+ 5DD2 – 2D ) z = e'*2* + Vy + +2x +Vy +x. |

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Q: Obtain the general solution. (xy + x) dx = 2 2 y + x + y¯ +

A: The given differential equation is…

Q: Find d2y/dx2 implicitly in terms of x and y.

A: To findd2ydx2

Q: b, y" -zy'-3y= e*

A:

Q: f (x) dx 21 and g(x) dx 14, find 3f (x) + 5g(x)] dx.

A: ∫09f(x)dx = 21   ∫09g(x)dx = 14∫093f(x) + 5g(x)dx = ?

Q: |f(x) dx g(x) dx = 15, find / [3f(x) + 5g(x)] dx. If 28 and

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Q: (x + 2y – 1)dx + 3(x + 2y)dy = 0

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Q: f(x)=10/17sqrt(6x^2+2x+6)= 10(6x^2+2x+6)^1/17, then df/dx =

A: f(x)=106x2+2x+6117

Q: Check that y Cx) = e* is the Solution of y" + y' - 2y = 0

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Q: What is the solution for y(t)?

A:

Q: Find the solution. d3x d?x d³x dx + 2 =0 dr3 dr? dt

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Q: +2x (D³ – 4D’D'+ 5DD" - 2D") z=e** + Vy +x.

A: Given PDE is D3-4D2D'+5DD'2-2D'3z=ey+2x+y+x We can write it as D-D'2D-2D'z=ey+2x+y+x             (1)…

Q: d²y B Show whether y = Ax² + · x2 is a solution for x2- dy + x dx + 3y = 0 or not. dx2

A: If y=Ax2+Bx2 is a solution for x2d2ydx2+xdydx+3y=0...(1) then it satisfies equation (1).

Q: y (x°y³ + 2x² – y) dæ + x³ (wy³ – 2) dy = 0| -

A:

Q: If f(x) dx = 3 and f(x) dx = 4 what is the value of %3D 5f(x) dx?

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Q: The f ²-3)³ dx is equal to x2

A: Given: I=∫x2-33x2dx For evaluating given integral, first we simplify given expression then integrate…

Q: of dx forf = 3x² y² – 4.x³ y Q2. + -

A:

Q: Find the general solution to: 3X y^ - Gy' +Qy= x*e*

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Q: px + qy=z-a √x² + y² + z²

A:

Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: 9. If f(x) dx = 35 and g(x) dx 14, find | [3f(x) + 4g(x)] dx. %3D

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Q: Find the solution. dy x-+ 5y =2r2y4 dx

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Q: If y = x3 – 2x2 + 3x – 1, then d2y/dx2 is equal to

A: topic - derivatives

Q: Then E(((X + 2Y)'D is equal to:

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Q: The answer for x is correct but the answer for dy is wrong.

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Q: 4-y² ²) dædy 2 2

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Q: (e) x = 4 – z2 - (f) x² – y² + 4y + z² + 2z = 0

A: x=4-z2 is a paraboloid and its graph is as follows

Q: f (x, y) = x² + 3y² + 4,

A: Supposing the question is asking to find the local minima value.

Q: 8 If f(x) dx = 37 and g(x) dx = 12, find %3D [2f(x) + 4g(x)] dx.

A: Given ∫08f(x)dx=37 and ∫08g(x)dx=12We have to find ∫08(2f(x)+4g(x))dx

Q: -2 S.f(x)dx -4 a. b.5°2f1x) dx C.5f(x) dx

A:

Q: (x = s² – t² y = s·t³ z = 2x – 5y,

A: See the attachment

Q: If fF · df = [cl-3x – 4y³ ) dx + (x²y) dy, what is F? F =

A:

Q: Find the particular solution of (d2y/dx2) = 4x3 - 2x; y' = 4/5 and y = 1 when x = 1

A: Given differential equation, d2ydx2=4x3-2x       ...(1) y'=45 and y=1 when x=1

Q: Find formulas for dy and Ay if y = x² – 7x + 3.

A: To give the formula dy = f'(x) dx and    ∆y = f(x+∆x) -f(x)

Q: Find E[Y(z)] when Y(z) is given by 2z' + 6z² + 5z + 1 2(2z + 1)

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Q: Q = - ST 8-x²-y² x² + y² y dz dx dy

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Q: Determine the value of C if f(x,y) = C is the solution of (x+ 2y-3)dx+(x+2y+1)dy3D0 for x=94 and y=…

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Q: Obtain a particular solution for + + +y = x³ + 2x + 1 dºy, d²y dx4 dx²

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.