5. (D² – 1)y = 0

Q: Z4 =:₂₁ (4x²yz - dz dy dx S₁

A: Given ∫23∫-14∫104x2yz-z44dz dy dx ∫23∫-14∫104x2yz-z44dz dy dx=∫23∫-14∫104x2yz dz dy dx -…

Q: 7/2012 - y x² + y² (²) di dx + (ye³ +2²) dy = 0

A:

Q: (x-2) (x³-4) Vx² +1 dy 1. If y = then equals to : dx

A: Please go through the attached solution. I hope that it  will help you .Thankyou . Best regards.

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: 5. y(x³e*y – y)dx + x (y +x³e*Y)dy = 0

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: 2 5+4y³ Evaluate f,* S* y dz dx dy

A:

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

A:

Q: B) dy = 8xex2. 9) y = e4x² + x A) dy = 8xe2x + 1 dx B) dy = 8xex2 + 1 %3| C) dy = 8xe + 1 D) dy -…

A:

Q: Solve the initial value problem.

A: The initial value problem: dydt=2t+9t2, y1=2

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: dy ニ 3 x +y-2

A:

Q: 5. (1+2xVx2 - y² )dx-(2yVx2-y? )dy =0

A:

Q: a) |(w - 1)(2y + 1) dy

A: a) ∫02(y-1)(2y+1)dy=∫02(2y2-y-1)dy=2∫02y2dy-∫02ydy-∫021dy=2y2+12+102-y1+11+102-y02…

Q: find d^2y/dx^2 if y= 17/ x^3

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Q: 4.Jy2-プdy

A:

Q: 25y2-4 dy 415 S. 2/5

A: ∫254525y2-4y dy Put, y=25secθ Differentiating with respect to θ, we get ⇒dydθ=25secθ tanθ⇒dy=25secθ…

Q: 1-Vy dy Vy 4

A: We need to find the given integral.

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: Evaluate the integrals

A: To evaluate, ∫01∫03-3x∫03-3x-ydzdydx

Q: Find the general solution of hp dy + 12- dx² dx 8y = 21e2x | dr3

A: To find the general solution of the given differential equation: d3ydx3−6d2ydx2+12dydx−8y=21e2x

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

A:

Q: -2x y" + (e by = 0 (e-* = z) -

A:

Q: Find the general solution of the followin d² y equation 5 + 4y = 8 +5. dx2 dx

A: General solution is sum of particular integral and complimentary function.

Q: Find dy/dx if y = u5 - 2u3 + 8 and u = x2 + 1.

A: Given function are: y=u5-2u3+8......(1) u=x2+1......(2) The objective is to find the value of dydx.

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

A: To findd2ydx2

Q: Calculate (ay² + y) dy dæ. 3.

A: We use the properties of integrals to evaluate the given integral.

Q: -4x-2 FInd given y =-2 dx Sx+3

A: By using partial differentiation.

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

A:

Q: -dy (49 – y2 )

A:

Q: 5 To-4x D 5-2x NILS (6z²) dz dy dx

A: solution:-∫052∫010-4x∫05-2x-y26z2dzdydx=∫052∫010-4x∫05-2x-y26z2dzdydx=∫052∫010-4x6z3305-2x-y2dydx=∫0…

Q: (4) (b) 10tsin(5t²- n/4)dt (4) (c) S 12(x³ + 2)ex¹+8x dx

A: We have to evaluate the integrals.

Q: dy 6. if y = (1+x²)etan-1x

A:

Q: d²y dy + 3x+y = 4sin (In(x)) dx²

A: Given Euler differential equation is: x2y''+3xy'+y=4sin(ln(x)) Let us take x=ez Replace:…

Q: Q5. Evaluate ſ^₂ ¹¹ xy dx dy. ry+1 y²

A:

Q: 2. Find the general solution of dy d²y dy + 12- dx - 8y = 21e2 - - dx3 dx2

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

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Q: Find dy/dx2 implicitly in terms of x and y. x*y – 6x = 9

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

A:

Q: 15. If y3 – xy = 5 ,1 d²y then dx2

A: y3-xy=5

Q: •7 49–x² r83–x²-y² x dz dy dx %D 0, -15+x²+y²

A: I am attaching image so that you understand each and every step.

Q: Vy2 -25 dy S y3

A:

Q: 9-y dy 5. S y

A: We will use trigonometric substitution.

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

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Q: 5) SOLVE dy _ yz %3D x2

A: A differential equation is an equation in x,y and derivatives of y. An ordinary differential…

Q: -3 -2 ²₁ ² [z³(x + y)³] dz dy dx

A: