D = (z + 1)(z – 1)(z² -

Q: D Exponential Shifting Theorem 4 (D° + 4D°-3D - 18)4=24x°e-3× t 4D²-3D - 18)y = 24 x°e¯*

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Q: Find the real valued general solution of y" + 5y = 0. %3D

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

A: Implicit differentiation involves the treatment of one of the variables as a function of another and…

Q: 2. -1z"cosdz zl=1

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Q: if z=x+iy then zz= 3- y² +1 3- y² – 1 G- ² |

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Q: Solve the linear system

A: 2x+3y=4x+2y=3over Z7

Q: b) y =1+ f(z)=2x-2 O 1ks f-(z)=-1 O 2 34s (2)=2x-1

A: Step 1 Replace y with x and x with y  Step 2 Then solve for y in this equation  Step 3 Replace y…

Q: X1, X2 2 0 12. Minimise Z = 60x1 + 80x2 bo Subject to 20x +30x2 2 900 40x1 +30x2 2 1,200 X1, X220 LO…

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Q: Find the 2nd solution using reduction of order. t²y" - 4ty +6y=0;t> 0; y₁=t²

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Q: Find the general solution of (xy² + x²)dy + a. 3xy + y3 = C b. 3xy - y3 = C xydx = 0 с. -Зху - уз с…

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Q: a z = 4x³-6x²y²-y com x= 2sen(t) y=-3cos(t) e

A: #As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: If xy2 3x2y + C, then what is the value of C at (2,2)?

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Q: 2 c4 e-x-2y dydx 2х

A: It is double integration problem

Q: 2 Find dyif y.+3x-7 and x =, 2t +1

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: 7. f (1, y) = z + y subject to z² – zy + y² = 1

A: Let h(x, y)=x2-xy+y2. Then we have ∇h(x, y) = (2x-y, 2y-x) and we also have ∇f(x, y)=(1, 1). Let the…

Q: x" + 2x' + 8x = 2e-2t - e-t,x(0) = 1, x'(0) = 0

A: Given differential equation, x''+2x'+8x=2e-2t-e-t,x(0)=1,x'(0)=0 The objective is to solve the…

Q: Q5/ find y', y=In(Inx) * O y'= 1/( x-2x)*(2x)=1 O y = 1/( x-2x)*(2x)=2 none of the above

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Q: nd the general solution to: 2yy -e^ = 0, |

A: The question is taken from the calculus in which we have to find  the general solution of  given…

Q: +2x (D³ – 4D’D'+ 5DD" - 2D") z=e** + Vy +x.

A: Given PDE is D3-4D2D'+5DD'2-2D'3z=ey+2x+y+x We can write it as D-D'2D-2D'z=ey+2x+y+x             (1)…

Q: Calculate the LOS of y = -x² + 2x + 4 LOS is x = a is b is ,c is

A: We have to find the line of symmetry and values of a, b, c in the given question.

Q: a) z=-x² + y² c) z² = x² + 2y² e) x² + y²-z² = 1 b) z=-x²-2y² d) -x² - y² + z² = 1

A: match the following quadratic surfaces with the following equations (a) z=-x2+y2

Q: -4x e Find a particular solution to y" + 8y' + 16y= x3

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Q: Find the general solution of ди ди (y – z) + (x – z) ди + (2y – 2x) ду - az

A: The differential equation is given as (y-z)∂u∂x + (x-z)∂u∂y  + (2y-2x)∂u∂z = 0 We will solve it by…

Q: If x2 z2 + y² + xz3 = 3, then dz at the point (1, 1, 1) is: O b. Ос. - 3 d. - 3 Ое. f.

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Q: px + qy=z-a √x² + y² + z²

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Q: z = 2 24 z=Vx² + y² 2 FIGURE 9

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Q: O': Find the general yy' – 2y² = e²

A: A first order Bernoulli ordinary differential equation is of the form dydx+pxy=qxyn Where p(x) and…

Q: :Q3 Classify PDEs below и ди y2 и + и = ue 5x — - ду

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Q: Qs) y" + 3y' + 2y = e* – 3

A: See the details solution in below

Q: 1l y" + 4y' + 4y = e-2x %3D x2

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Q: + d²z Oy2 = 0;

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Q: (D^5-3D^4+8D^3+16D^2-9D-13)y=0 nonhomogeneous undetermined coefficients

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Q: - Q3): If xfx + yfy = nf show that x²fxx + 2xyfxy + y² fyy = n(n − 1)f

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Q: y = v1 - x2 from a = 0 to r = ;

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Q: Find the general solution to the homogenous DE y'-16у' + 64у %3 0

A: The given homogeneous DE is y''-16y'+64y=0. The auxiliary equation is m2-16m+64=0.

Q: A. Find dy 1. y = In V3x²- 9x +1

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Q: Solve the equation using Reduction of Order y" -y = 2et Oy=c₁e¹ + c₂xet + e* (x + c3e-²x + C4)…

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Q: = (y² – z² +3yz – 2x of the following is/a

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Q: The discriminant of ax2 + bx + c = 0 is defined by_________.

A: The given equation is ax2+bx+c=0.

Q: Obtain the general solution of the homogenous L.D.E (D³-14D+8)y=0

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Q: d'y dx2 (3y -1) 24y If y' -y = 2x prove that

A: Solution: The objective is to find the double derivative of the given function

Q: Express (2xy + 2x – 1) – (x² – y² – 2y)i in terms of z & z, then simplify. - -

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Q: f Lan 2X e *3 of +sec2X Pinel dy o

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Q: What is the discriminant of the PDE?    4d2/dy2=-3du/dx-4u

A: the discriminant of the PDE is :

Q: b. xy--2×y- ヴり C. 2x- xy - zy +> - xyy'+ 2xy'; when x 1 when X = 0, y-1 19=1

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Q: Does y =e9-x2-2 exist?

A: Given an equation, y=e9-x2-2. To check whether the equation exists or not. The value of e is…

Q: Find formulas for dy and Ay if y = x² – 7x + 3.

A: To give the formula dy = f'(x) dx and    ∆y = f(x+∆x) -f(x)

Q: y = (2x + 1)v2x+1

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Q: 18.t2y′′−4ty′+6y=0,t>0;y1(t)=t2

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