dy 1- J ++y2

Q: d²y 5. If y = 4sinx + x²cosx + 4x then find dx2

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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: 1 Q2: Evaluate fo y² (x² + y²) dx dy

A: Given :∫01∫01-y2y2x2+y2dxdy

Q: dy If 2y = xlnx, then dx (In x)xinx (xinx) In x (b) (d)(In x)xanx) 2

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Q: dy 5. -2ty + 4e-t² dt y(0) = 3

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Q: /1- (z² + y²) dz dy dæ ) Evaluate

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Q: Evaluate " " So s L dz dx dy rvZ c3y (8-x²-y² Jx²+3y²

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Q: x²V4x +1 dy then dx If y = In (x³ + 5)3

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Q: d'y 2y If x + y = xy, show that dx2

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Q: 1-x² 2. , S. et²+y? dydx = (е-1) 4

A: We have to show that:  ∫01∫01-x2 ex2+y2 dy dx=π4(e-1)

Q: x² dy = x*y% + xy - 3

A: This is reccati differential equations, but this can be solved in simple way.

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: dz Find - if z = (9x + 5y)°. dy

A: we can find the derivative as below

Q: Find ax dy x-2–1 given y = 2x3

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Q: -x ôx ô -0, ây for z = tg(xy)+. y

A: Prove that for z=tgxy+xy, x2∂z2∂x2-y2∂z2∂y2+x·∂z∂x-y·∂z∂y=0.

Q: d²y dy +2 + 5y = 5t2 dt? dt

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

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Q: xydæ – (x² + 3y²) dy + 3y?) dy = 0

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Q: y" - 4y'+ qy = t %3D y (0) =o y' (0) =1

A: Introduction: A higher-order linear homogeneous or non-homogeneous equations with given initial…

Q: A. y(x² + y²)dx + x(3x² – 5y²)dy = 0; whenx = 2,y = 1.

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Q: find dy. 2y3/2 + xy - x = 0

A: we have 2y32+xy−x=0

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

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Q: Q3: van fy = xy-1+ x.ln(x) J f(x,y) = x' + y* if it was

A: To find the partial derivative

Q: Find dy x 3 In (x - y) = xy + y²

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Q: Evaluate -5у-5 dy 31. Jv+2y-4

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Q: 4. 2ydæ + (x - x°y) dy = 0

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Q: Find dy/d 5x²+xy+ N9 - Say %3D =D0

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Q: z = xy³ – a²y, x = t² + 1, y = t2 – 1

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Q: 8y dy e2y

A: topic - definite integral

Q: 1. . 2 y² +4 - dy y

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Q: y (x°y³ + 2x² – y) dæ + x³ (wy³ – 2) dy = 0| -

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Q: /1- 7y² dy

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Q: Evaluate [ T 1-x² x² + y² dydx.

A: Given: The integral is ∫022∫x1-x2x2+y2dydx. The aim is to evaluate the given integral. Concept:  The…

Q: 1. If (x and jy) = 3 + j8, find x and y.

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: EZ = X +Y if X,Y are

A: X follows normal distribution with mean 0 and variance 1. Y follows normal distribution with mean 0…

Q: d. {(x, y)| y = 3x – 8} {cx, y)ly = } x+3 е. %3D x-5

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Q: 1 S² = y e2y dy

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Q: find dy,if y= x²+2)Cx*+3x+) %3D

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

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Q: -4-sy=0, y(1)=0, y'(1)=2 b) dt

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Q: find dy. y = x3 - 3√x

A: Given:         y=x3-3x Solve y for dydx Use the formula: ddxxn=nxn-1

Q: Find dy/dr If x²(x = y)² = x² – y²

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Q: 18. (9x D² + 3xD + I)y = 0, y(1) = 1, y'(1) = 0

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Q: dy 1 ax x2 -4 y = 1

A: I have gotten some difficult integration so i left as it is

Q: (x = s² – t² y = s·t³ z = 2x – 5y,

A: See the attachment

Q: dy if y = In dæ 3x + 2 \ 1/4 22. Find x2 – 5

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Q: 18.t2y′′−4ty′+6y=0,t>0;y1(t)=t2

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