y" +7y' +12y = 0

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

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Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

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Q: e particular solution of the differential uation x^2 dx - (y+1) dy 0 if y(0)=1 2y^2+3y-6x^3+6= 0…

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Q: solve using Separation of Variables. dy dt = ry-3

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

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Q: Find the particular solution for (2y - x) dx + 3xy2 dy = 0 when x = 1, y = 1

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Q: Obtain the particular solution satisfying the initial condition indicated. (variable separable) dx…

A: Use the variable separable method and satisfy the initial condition. Also use the properties of…

Q: dx ylnx- dy y + 1₂ X 2

A: given :ylnxdxdy=y+1x2

Q: Solve the differential eqyations (3x +5y +4)dx + (5x +3y +6)dy =0

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Q: 3. (16x + 5y)dx + (3x + y)dy = 0 1 (Cos 2y - 3x²y²)dx + (cos 2y - 2x sin 2y - 2x'y)dy 0 the

A: In the given question we have to find the solution of the differential equation 1.…

Q: Find the general solution for -x) dx - (-y) dy dy = 0

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Q: . Find P.S. of (16x +5y) dx + (3x+y) dy = 0 of the curre to pass thru the point (1,-3) 2. Find P.S.…

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Q: 15 dy dt 2-

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Q: 1 dy J yi + 3y² + 1

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

A: Given : Differential equation cos 2y - 3x2y2dx + cos 2y - 2x sin 2y - 2x3ydy = 0   To find :…

Q: dy -X+Y

A: The solution to a linear differential equation of the form dydx+Py=Q, where P and Q are functions of…

Q: 11. Find the length of the curve x = on the interval [2, 4] (integrate with respect to y) 12y3

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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: Solve for Txyz given the function T(x, y, z) = z tan (In x - √y)

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

A: We will find out the required solution.

Q: 7. What is the order, degree and linearity of: (dy + 3x dx, d°x = ey dx3 8. What is the order,…

A: Note: since you posted multiple questions. As per our guidelines we are supposed to solve one…

Q: Obtain the particular solution of (3siny-5x)dx+2x^2cotydy=0 using Bernoulli's Equation. (Complete…

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Q: 6. If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: The given equation are x=y3-y,dydt=5  and y=2.

Q: Find the particular solution for the given separable equation when y(0) = 3. 1 dy = ysin(2x) 1? dx

A: To find the particular solution for the given separable equation when y(0)=3

Q: find dy/dx

A: y=∫sec x21t2+1dt.

Q: 2 In sec Vi + tag V + C sec sec z dz %D

A: 35. given integral,∫sec x . dxx = 2∫sec x12 . 12x-12dxlet x12 = u⇒ 12x12-1 dx = du⇒12x-12dx = du

Q: Aiz (1) i i v, ~ Vz =o iv, - t= 0 i U, =t -i?v, = -it

A: The first highlighted portion is -i2v1=-it. To make the coefficient of v1 equal to 1 in the previous…

Q: Estimate Ay using differentials. .1/3 y = x¹/3 e³x-1, a = 1, dx = 0.1 -

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Q: 13. dy/dt = y²(1-y)², -∞ <yo <∞

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Q: Intergrate:

A: To evaluate the integral.

Q: 3z cos(z)dz

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Q: 23. (4y + 2t – 5) dt + (6y + 4t – 1) dy = 0, y(-1) = 2

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Q: y(1-x^2) dy/dx=x(1+y^2) solution of first order Deferential Equation

A: We have to find solution of y(1-x2)dydx=x(1+y2)

Q: 1. ydx + 2x dy - y2x² dy = 0 dy 2y

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Q: solve using homogenous and exact. (2x-3y)dx+(2y-3x)dy=0

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Q: Solve for y + In lyl at x=6: y'=(yx^2-y)/(y+1); y(3) = -1 4.5

A: The given differential equation is y' = y x2 - yy +1  with initial condition y ( 3 ) = -1. To solve…

Q: tion of the separable equation dy 23 3 +2)³ + 2)?

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Q: tion to (1+ x²) dy + 2xy = 4 that satisfies the initial condition y(0) = 0. dx %3D %3D

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

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

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Q: 1. d²y dy +6- dt² dt +8y=-4 cos(3t)

A: We need to solve D.E. As per Bartleby's guidelines we can solve one question from multiple question.…

Q: dy 3 (49-y²) 2

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

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Q: x dy + y dx = 3x²y² dx, y(-1) = 2

A: Rewriting given differential equation into standard form of bernoulli equation

Q: 1) (2cos³xsin x – ysin x – 1)dx – cos x dy = 0 ; when y ) = 3v2

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Q: 4. (4y+ 21 - 5)dt +(6y+41 –1)dy = 0, y(-1)= 2 cs

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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/dx=x2+3y2/2xy

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Q: *= 1+?-,y = -x²,x > 0 2. = x³(y – x)² +2, y1 = x,x > o у 1. %D = x³ (y – x)2 + dx , Υ1 - x, x > 0 dy…

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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.