1) (у? — ху) dx + x?dy %3D 0 Ans: y = Inx + C

Q: Find the general solution of d²y dy 4- + 4y = 0 - %3D dx?

A: The given differential equation is d2ydx2-4dydx+4y=0.

Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

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Q: Find dy Y= 5In CI+x") 4 dy'=?

A: The solution are next step..

Q: Find the set of solutions (3x – 3y – 2) dx – (x – y + 1) dy = 0. - - %3D

A: Given differential equation is linear, we will use substitution to solve it

Q: 3. II Azy'dz dy = 2y°(3² – 1)dy | 2y (y? – 1)dy 1

A: Given that a double integration .We use general  property of integration to solve this integration.…

Q: Find the particular solution of y (9x - 2y) dx -x (6x - y) dy=0., when x=1, y=1. Let x=vy

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Q: What is the integrating factor of the equation (2xy*ev + 2xy³ + y)dx + (x²y+ev – x²y² – 3x)dy = 0 A…

A: We have to choose the correct answer from the given option according to the given condition

Q: 2 1. Evaluate 8x" dx by the Gaussian quadrature method. 7

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Q: Obtain the solution using Integrating Factors Found by Formulas y(y + 2x − 2)dx − 2(x + y)dy = 0

A: Find your answer below

Q: 5 If y = dy then dx %3D x+1

A: Given that: y=xx+15

Q: (Зх — у — 4)dy — (х + у— 4)dx %3D 0 - -

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

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Q: 2²ye+v°-²dx dy dz 1 -1

A: We have to calculate the integral.

Q: 2. у(у+ 2х — 2)dx — 2(х + y)dy 3D 0

A: A differential equation of the form M(x,y)dx+N(x,y)dy=0 is said to be exact iff, ∂M∂y=∂N∂x

Q: Use a suitable method  to find the solution of (1-x^2)(1-y)dx=xy(1+y)dy

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Q: dy 4 – 5y = e-3t sin(4t) ; y (0) = 3, y (0) = 10 dy %3D - dt?

A: We solve the given IVP  y"-4y'-5y=e-3tsin(4t)........(1) y(0)=3, y'(0)=10.......(2)

Q: What is exact solution for dy/dx =(x2+y2)/(x+y)

A: Given: The given equation is dydx=(x2+y2)x+y

Q: 7 xsiny dx + Cx²+1)cosy dy = 0, yC)=TT/2

A:

Q: I. Solve for the General or Particula 1. dy dx = 3x+xy² y+x²y

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Q: S (sech*y – sec®y) dy

A: I =∫ (sech4y -sec6y) dyI=∫ sech4y -∫ sec6y dyI=∫ sech2y (1-tanh2y) dy       -∫ sec2y (1+tan2y)2…

Q: S csc“(3y)dy

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Q: integrate the following ∫(y-2 + 1/2y - 1)dy

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Q: 5. (1— ху)-?dx + [y? + x?(1 — ху)-?]dy %3D 0

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Q: 1) (22 - ry + y?)dx - xydy 0, where y(1) = 0

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

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Q: 1) CSc y di + secx dy =0 CSC y Y.

A: Given query is to solve the differential equation.

Q: (2,5, – 6) | 16x dx + 4y dy + 2z dz (0,0,0)

A:

Q: Intergrate:

A: To evaluate the integral.

Q: Find the particular solution from y(9x-2y)dx-x(6x-y)dy=0  when x=1/3 and y=5/2.

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Q: 5. S , dz dy dx 2 c3

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Q: 4- S" e-x* dx 5- Vy e-y² dy

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Q: ху+3x- у -3 dy %3D dx xy-2x + 4y- 8

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Q: 2. Integrate dy (a) Vy* +16 (b) |6x – x² dx

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Q: 22 32 S[ (4-y ) dydx 1. ans:- 3 0 0

A:

Q: 2-dy dy. y2 dx 12 ナ /2

A: We have to solve the given equation. The given equation is 2-dydX=y2X2+yX+1    ......(1)

Q: Find the particular solution of y(9x-2y)dx - x(6x-y)dy= 0, when x=1, y=1. To start, let y=vx.

A: The given differential equation isyax-2ydx-x6y-ydy=0, with y1=1It can be written…

Q: 4(3x+ y – 2)dx – (3x + y)dy = 0

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Q: 3. (х+1)dy %3D (2хe* - ху- 2у)dx

A:

Q: 3. a) If y = 6x - 5x +7x +2x – x+10, find dy at (2,3) i. dx d'y il. -at (1,-5)

A: See the attachment

Q: Solve = 1 +y, y(0) = 0 by Picard's method. %3D dx

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Q: 1 y2e- dy 7 صواب ihi

A:

Q: 7 5-y y dx dy 3y

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Q: Integrate both sides dy `xdx

A: We have ∫dyey =∫xdx The general rule if integration says: ∫xndx=xn+1n+1

Q: Obtain the general solution to the equation. 3. dx - (у — 2ху)dy

A: Topic - differential Equation

Q: I sin 2 dy dx (x² – y) dy dx 5. 6. x? – y² dy dx 8. L ellyt dx dy 7.

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Q: 1) S 2 sec y (tany – sec y) dy

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: dy dt II

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Q: The solution of (1 – y² )dx + (1 + x² )dy = 0 is: %3D

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Q: 2. メ +ッ 2. dy- X. dx

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Q: Show that the antiderivatives are equivalent.…

A: ∫6/(4 + 9x2)  dx = arctan 3x2 + C or arccsc √(4 + 9x2 ) / 3x + C We need to show that the…

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.