e2x2 f (y) dy +g (y). C) u (x, y) =e2.2 f (y) dy +g (x). The solutions of the PDE Uyx - 4xuy = 0 depending on x and y are of the form A) u (x, y) =S e2r (7) dr+ g (y). B) u (x, y) =e4ry f f (y) dy +g (x). D) u (x. y) = c2sS() dy +g (y) . E) u (r, y) =feruf (r) dr + g (y) .

Q: Q1: Write down the form of the particular solution of: y(5). 3y(4).y(2)+3y(1) = x² + xe *

A: The given differential equation is: y(5)-3y(4)-y(2)+3y(1)=x2+xex

Q: The general solution of (D³+4D)y=0 is (A) Ay=c₁еx+c₂e²x + c3e² (в y=e*(c₁cos2x+c₂sin2x) -4x y =…

A:

Q: Differentiate with respect to x: 3x4 x³y + 4y³ = 6 Select one: the following implicit equation for…

A: implicit derivative of y(x) for 3x4-x3y+4y3=6

Q: Find the general solution of the DE (2y – x2) dx + (y+2x) dx=0 А) 2ху + 3 y2 =C 2 (в) 2ху — 3 x3 y2…

A:

Q: What is the general solution of xy(xy5-1)dx + x²(1+xy5)dy=0 ?

A:

Q: Find the general solution y(x) of ry + 3y = r².

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Q: xux − yuy + y²u = y²

A:

Q: y²dx + x(x+y) dy=0

A: This is a homogeneous differential equation.Substitution x=vy .

Q: f (x, y) = − x² - y² +3. :

A: We have to find the maxima of the function  f(x,y)=-x2-y4+3

Q: If y =√x + √y (a) (c) y + x y² - 2x 3 y³ + x 2y² - x + x + y+...∞, then is equal to dy dx 3 y³ – x…

A:

Q: y3 (x+c)e* is a solution of y-y3e"* A True B False

A: To show y=(x+c)e-x                     (1) is a a solution of y'-y=e-x                      (2) Then…

Q: (D2-3D + 2)y=e5x, Find Y = Yc+ Yp O a. 1 *C₁² + €₂²¹ +2³² 12 O b. ³² C₂₁ ²² +₁₂=²+ = 12e-² -5x 12 O…

A:

Q: The general solution of the D.E. (x³ + 3xy²)dx + (3x²y + y³)dy = 0 is a. (x² + 6x²y² + y4) = c O (a)…

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Q: 1 (D² – 3D + 2)y 1+e¬x

A:

Q: 2x- (ii) Given aty=b²x-y and a 4x+3 = bx-5y, show that 3y-6x=7x² +5y²

A: (ii) Given ax+y=b2x-y and a4x+3=bx-5y We will use logarithm properties to solve the given:

Q: Here R^3 - {(0,0,0)}. please proof this using submersion. thank you.

A: Given: R3=(0,0,0) To find: The set M=(x,y,z)∈R3:x2+2y2+z2=4xyz a submanifold of R3.

Q: Find the general solution of (y + 1)dx + (4x - y) dy = 0 Show your solutions on a separate sheet of…

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Q: dy The solution of (1 – x²) + ху %3 ах is dx (A) y = a + c v1-x* c Vi-x² (B) y = a - c v1-x² (C)…

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Q: y²dx + x(x+y) dy=0 A xy²=c(x+2y) B x²y=c(x+2y) C xy²=c(2xy) D x+y²=c(2xy)

A: Let us consider the differential equation of the form dydx=f(x,y). Such that f(x,y) is a homogenous…

Q: Show that y %3D Cіx-1 + С2х + Cзlnx + 4x2 is a solution to x3y" + 2х?у" — ху' + у %3D 12х?.

A:

Q: What is the general solution of xy(xy5 −1)dx + x²(1 + xy5) dy=0 ? A 2x³y³-3x²= Cx² B 2x³y5-3x²=Cy²…

A:

Q: If the given three vectors are coplanar, then find the value of x. A = i-2j + 3k, B = xj + 3k, C =…

A: A, B, C are coplanar.So

Q: (D² – 3D + 2) y = (1+e*)? -

A: We need to solve- (D2-3D+2)y=(1+e-x)2 General solution is given by- General solution = Complementary…

Q: (D² – 3D + 2)y = e2*(1+e2x)

A:

Q: (D2 - 3D + 2)y=e5x, Find Y = Yc + Yp O a. O b. O C. O d. C₁e* + C₂e² + 1 2r 12 e -X C₁e + C₂…

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Q: If y = f(x) is the solution of (72°y – 16x7 – 2y®)dx + (x7 +7y® – 12ry")dy = 0, f(0) = 0, then %3|…

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.