d?y dy 2- 8y = 8x? + 20x + 2, at y(0) = 0 and y(0) = -8 dx? dx

Q: dy and d²y if x = t and y = 3. Find dx dx? 1+t 1+t

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Q: dy/dx - y = xy5 = 0 Ans. 1/y* = -x++ ce 4*

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Q: За - За - у 314 а^ За '(x² + y? ) dx (b) 2a S" L (x² + y²) dy dx Ans. (a) [" dy [V" (1² + y²) dx +…

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Q: 8. y dx = (3x + y³ – y²) dy; when x=1, y=-1

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Q: dy 3. Find dx? .2, Given that xy + x²y° = 5.

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Q: d'y dy -4- 4- dx? dx -3y=0. y(0)=1, y(0)=5

A: According to the given information, it is required to solve the given differential equation.

Q: a. (2ry*e + 2xy + y) dx + (r²y*e -x²y² – 3x) dy = 0; when x = -1, y = 1

A: As per our guidelines we are supposed to answer 1st question only. Please repost rest questions...…

Q: dy y- dx2 dy dy = 7(y+1) dx? dx

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Q: y(2x? - xy + 1) dx + (x - y) dy = 0, ANS. y(2x – y) = c exp (-x?).

A: Given differential equation is y(2x2-xy+1)dx+(x-y)dy=0

Q: = y - dy 3. 25 @ y (0)=1, y (0) =2 dx2 dx

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Q: Find dy/dx and d²y/dx2 for r = t2 +t +1 and y = t2 + 2t - 1.

A: given that x=t2+t+1 and y=t2+2t-1 we have to find dydx and d2ydx2 Now,          dydx=dydtdxdt…

Q: Find dy/dx in terms of a and y if x?y – x - 4y – 10 = 0. dy dx

A: To find the derivative w.r.t x using implicit differentiation.

Q: (x+ x+)dx + By xdy 2. (3x-y-4)dy - (x+y-4) dx a0 1. when XE4, Y=

A: Topic:- differential equations  Note:- as per our guideline if more than one question uploaded than…

Q: dy Q2 Find dx of x = *-Y 2 x+y

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Q: y-dx + (x2 + 3xy+ 4y²) dy = 0, when x = 2, y=1

A: Explanation of the answer is as follows

Q: d*y + 6 dx3 d y d?y 4. dx2 dy 6 - y = 0 dx+ dx

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Q: d?y Calculate dx2 y = e-X + eX d?y dx2

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Q: d'y dy -35 +y=0 2.x dx? dx not defined 3 O 2

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Q: dy with y(0) = 1 dx y – 3 II

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Q: dy Find dx given that +y - 5y– x² = - 4.

A: Given,            y3+y2-5y-x2=-4

Q: dy dx What is y(2)? Suppose = 6x² + 2x − 3 and y(0) = 4. - oy(2) = 14 oy(2) = 16 oy(2) = 18 oy(2) =…

A: The answer is given below:

Q: dy/dx + 2xy + xy = 0 Ans. 1/y3 = -;+ 1 + ce3x? 2

A: The given differential equation is  dy/dx + 2xy +xy4=0

Q: d²y 3- 33+ 10y = 0 dx3 dx? dx

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Q: d²y d'y (k) 을-42+13y =0 (1) "+2+y = 0 dx dx? dx dx? d? (m) dx (n) 9 +16y=0 d'y dx?

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Q: Q3/ B: Classify then solve d'y dy (x + 1)? + 3e* dx dx

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Q: C. dy b. 4 sin 2x> , y = 2, when x = 2 %3D dx dy С. dx = x + 3+ e2x>, y = -1, when x =

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Q: d?y dy 3- 4y = 0 dx? dx

A: Solution of a differential equation

Q: y = sinx + x² to dy dx? x² y +2

A: Given, y=sinx +x2 Differentiate two times with respect to x to get required differential equation.

Q: dy d²y d³y Find and from: dx ' dx? dx3 1. x = cosh t and y = csch t

A: Please see the below pictures for detailed solution.

Q: 1 d'y dy + 5y = 0, subject to y(0) = 0 and y'(0) = 40 dx 4 dx2

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Q: d'y dy and y-(x3+2x-1)1/2 find dx dx

A: Given, y=(x3+2x-1)2we need to finddydx andd2ydx2

Q: 24. dy + y = 12r; dx r + 2r dx dx

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Q: d*y dy is dx x dx ferential

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Q: (yæ² + æ*) dy – (y³ + 2 y² a 3 3 y x²) dx = 0 - - –

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Q: Sõlve: d²y Y- dx? d²y + = 7(y+1)- dx? dy dx

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Q: dy Determine the solution of = 8 – 3y given y (0) = 12 dx

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Q: d?y dy 6. + 8 +2 y = 2x²e* + 4 cos (x) dx2 dx

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Q: Find dy/dx and d²y/dx2. x = e*, y = te-t

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Q: Ε. = Oy dx 47&a• (x +y)3 2

A: Introduction: The definite integration is the integration where we put limits over integration.…

Q: Evaluate dy/dx from the equation 3xy^2 + 4(y/x) - (y-5)/(2x^2 - 1) = 11 when x = 1.

A: Given equation,  3xy2+4yx-y-52x2-1=11 Differentiate with respect to x

Q: d'y dx dy 6. 4Y-4 +5y = 0, y(0) = 2, y'(0) = 4 dx

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Q: 4xy dx + 2x²° dy + loy - dx + 15 x y dy=0 t

A: given equation 4x2y dx+2x3dy+10y-dx+15xy dy=0 claim- Find non- exact or first order linear DE

Q: d?y 7. y = e2" – 3e-, dx? dy - 2y = 0 dx

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Q: dy when x = 1. dx If y = u" and u= 6x +6, find (Simplify your answer.) dx x= 1

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Q: dy = a-x dx when x 1, y = 2 when x = 2, y = 0 %3D what is the value of a?

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Q: d?y dy + 4- 2- +12 y 2x2 sin(x) - e2x dx2 dx

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Q: d²y dy dy %3D 1 2. dx2 6y = 0, when x - 0, y = 2, - %3D dx dx

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Q: dy dx + 4y - e* = 0, dr y(0) = 4 3

A: Given: dydx+4y-e-x=0, y(0)=43

Q: d'y Find dx2 (a) y = 8x³ – 5x² + x dy dx? (b) y = 7x² – 2x + 9 - dy dx? x + 6 (с) у %— dy dx? (d) y…

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