-18e5t y" – 10y/ + 25y = t² +1 Yp ||

Q: 9. dy/dt = y²(y² - 1), -∞ < Yo <∞

A:

Q: Ex. Find the general solution to dy 1 -2.x dx X -

A:

Q: + 1 =2e- dy

A: Given, Can be rewritten as

Q: Find P.S. of (16x+5y) dx + (3x+y) dy = 0 If the curre to pass thru the point (1,-³)

A: The given equation is: (16x+5y)dx+(3x+y)dy=0⇒(16x+5y)dx=-(3x+y)dy⇒dydx=-16x+5y3x+y⇒dydx=-16+5yx3+yx

Q: 8. (D2 – 10D + 34)y = -cos3x

A: Answer and explanation is given below

Q: 3 9 dx dt -1 -3 with x(0) : 4 Give your solution in real form. X1 = X2 = 2. II

A: The objective is to solve the differential equation:

Q: dx dt -1 -3 [:] 2 with x(0) 4 Give your solution in real form.

A:

Q: G3- y²sinx+3e3*)dx+(3xy² +2ycosx+)dy=0 |

A: In this question, we have a differential equation of the form Mdx+Ndy=0 Here we have to check the…

Q: 1 В(т, п) ym-1(a – y)"-'dy. am+n-1

A:

Q: dy ху+3x-у-3 7. Ans: y-x+In y+3, %3D = C dx ху-2х+4у-8

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Q: 10.(x + Jy² + 1)dx – (y-- -(y- |dy = 0. y2+1

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Q: dy (2) Find at x =-1 if y = u³ + 5u – 4 and u = x2 + x dx

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Q: dy = ay + by", dt a > 0, 6 > 0, -∞ < Yo < ∞

A: A differential equation is given by, dydt=ay+by2 for a&gt;0, b&gt;0, y0&gt;0. The objective is to…

Q: 4.Jy2-プdy

A:

Q: 8. Jydx + (1+ x)dy = 0,,when x = 1, y = 4

A: Differentiable equation can be solved separating the variables on each side and then integrating…

Q: 6x-9 =? dy Sx + uy dt

A: Given system of differential equation is dxdt=6x-ydydt=5x+4y In matrix form, we can write it as…

Q: Find the solution of (x² – xy – y²) dx + xydy = 0 -- -

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Q: б бу-гу2 -14-292 y dx dy

A:

Q: Find P.S. of (16x +5y) dx + (3x+y) dy = 0 If the curre to pass thru the point (1,-3)

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: 3. fy dy + 10g = e + dt +7 -2t

A:

Q: 4. (D² – 10D + 34)y = -cos3x

A: Using method of Linear Differential Equations with constant coefficients.

Q: S(y* - y-3)dy

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Q: d²y 2) Obtain a particular solution for d*y dx+ + + y = x³ + 2x +1 dx2

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Q: -2dх 38. y-2dx dy er e2x + 1' УО) %3D 1

A:

Q: dy 2ty(y - 1) dt 3(1 + P):

A:

Q: dy 5. S: y(1-Vy)2

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Q: d² y dt² + 3 dy dt +2y(t) = 2e²¹ ; y(0)=0_

A:

Q: 1² + 3x + 4 If t = (r² – 1) what is dt/dx?

A: We have to find derivative

Q: Find dy x 3 In (x - y) = xy + y²

A:

Q: 3. (4r'y-15r-y)dt + (r +3y-1)dy = 0 CS Scanned with CamScarner

A: We can solve this using exact equation of differential equation

Q: Does the function y(t) = 6e-3t satisfy the initial value problemy '(t) - 3y(t) = 0, y(0) = 6?

A: We have to verify that y't-3yt=0, y0=6 where yt=6e-3t If t=0 then, yt=6e-3ty0=6e0=6 Therefore, y0=6…

Q: y² + 5 dy J y²Cy² + 25)

A: Given problem:-

Q: 5) If y- x-2x and at ts V2 Find dy

A: To find dy/dt at t=sqrt(2)

Q: 4. Compute (a)음(3e2-4) dx (b) 4 dt dx-x 1+t2

A:

Q: y et 2x *Sec2X Pinel dy o

A: By using these differential formulas that are ddxex=ex, ddxax=axlnx where a is constant,…

Q: y' + 4y = e^(4t) %3D

A:

Q: dy 6. if y = (1+x²)etan-1x

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

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Q: 4. ydx + x(Inx - Iny - 1) dy = 0, when x = 1, y = e

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Q: - 3-z2-y 2. Evaluate L* L z dz dy dx -5+x²+y²

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Q: Vy2 -25 dy S y3

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Q: d'y dy dy -+6 +11-+6y=4 dr dr dt y(0)= y'(0)= y'(0)= 0

A: Given the Ordinary differential equation:

Q: 5. ydx - (x +3y')dy = 0 Ans. x = 6y In C

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Q: (3x -y - 4) dy t (x+y-4) dx = 0, 2. 14

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Q: 4) Solve d²y + 4y = 2e¬t %3D dt2 Where y(0) = y(0) = 0 %D

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Q: -3 -2 ²₁ ² [z³(x + y)³] dz dy dx

A:

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.