3. Given: y = f (u) and u = g(x), find dy/dx: %3D 2u d) у 3 u = 10x² + x + 1 (u²+1)' e) y = u+ cos' -2 и, u = TX

Q: Suppose dy/dx = x- y and y = 2 when x = 1. Use Euler's Method with increments of Ax = -0.1 to %3D…

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Q: 7. Differentiate w.r.t x- sin 5x cos 3x 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

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Q: e) у- In 2 2xe dx 1 dx xcos(In x) /2 g) y= V1+cos4xdx

A:

Q: 19 271. dx y= 1-X) dy = -Ldx -dy= dx S-(-yei) y" dy 99 99 100 100 99 dy dy 100 %3D + R00 100 ). %3D…

A: Refer below

Q: 2. Find the value of dx at y=2 if x=z²+5z and z= (y² + 2y)²/3.

A:

Q: dy/dx=3x^2+1 with y(1)=2. Estimate y(2) by Euler's method

A: given differential equation dydx=3x2+1 with initial condition y1=2 claim- estimate y2 by euler's…

Q: 2. Z dx dy dz to

A: (5) Given integral is ∫02∫04−z2∫02−zzdxdydz.…

Q: Can you help me step by step?

A: According to the given information the given function is:

Q: When choosing u and dv, we want a u that will become simpler (or at least no more complicated) when…

A: The statement is regarding the formula for integration by parts.

Q: Obtain the general solution using separation of variables x cos² y dx + tan y dy= 0

A: Given differential equation is: x cos2y dx+tany dy=0 Apply variable separable: tanycos2ydy=-xdx…

Q: 7. (a) Find dy/dx, when x a(1 + cos 0), y = a (e + sin 0). (b) Differentiate xCOsx w. r. t. (cosx)*.

A: Proceed as shown below...

Q: 1- Evaluate: 2y sinx dy dx อน 2- If u = x² + ey², x = sin 2t , y = cost² find Ət

A: Above question is solved.

Q: (4, w/8) 1. (y cos xy dx + x cos xy dy) (0,0) (0,5) 2. e2* dx + ye2 dy) (5,0) (1,1) 3. 2(x dx +y dy)…

A:

Q: In(5x +3) dy at x = 0. dx (a) If y = then find et

A: Given; y = ln(5x+3)/e5x

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: (ylny-exy)dx + ( + xlny) dy = 0

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Q: 2,3 Given z = sin (x + y) where x = s²t, y 2s 3t. az as az at

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, compute y'…

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Q: 1) (22 - ry + y?)dx - xydy 0, where y(1) = 0

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Q: A rectangular plate with insulated surface is 10 cm. wide and so long compared to its width that it…

A: The two-dimensional heat equation is given by The steady-state heat equation without a heat source…

Q: 7. (a) Find dy/dx, when x = a(1 + cos 0), y = a (0 + sin 0). (b) Differentiate xcosx w. r. t.…

A: Differentiation using Logarithms: When a function appears as an exponent of another function we make…

Q: OBTAIN A FAMILY OF SOLUTION 2. (x - yny + y In x ) dx + x CIn y - In x)dy =0 3. [x - yarctan…

A: This question is related to differential equation.

Q: 2 1 Evaluate the iterated integral42x°y® dy dx. 56 -1 0 2 1 | 12*y®dy dx= [ -1 0

A: Consider the integral

Q: 2X Qul If y = Fird dy e %3D (x? +1) (I+ sinx)

A: We use logarithmic differentiation

Q: 8. When reduced to a linear DE of order one in z, bernoulli' equation dy/dx +y (1/x) =3x2y2

A:

Q: 21 Find Ez hox) Cx siny +y cosy)it hex cxcosy-ysiny) 5 aanon Ze o Pn hex) for which conserrabive on…

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Q: 4- Find dy/dx for y = 3l(sin-(e-3x')1² dy 1(-6x) = 3(sin-(e-3*" )I* In3 2(sin¬1(e¬3x²) dx In3…

A: Given y=3sin-1e-3x22

Q: 7. Obtain the particular Solution by satisfying the conditions indicated. 3x dy; when x = 2, y = -1.

A:

Q: 4. An earth satellite moves in a path that can be described by x2 72.5 = 1 71.5 where x and y are in…

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Q: - arctan(e**) dx =? 1+e2kx A) (arctan(e*)In [cos(arctan(e*)| + S In [cos(arctan(e*)da]+ c kekz B)…

A: Let I=∫tan-1ekx1+e2kxdx where tan-1ekx=arctanekx Put tan-1ekx=t…

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y)=3x<y becomes dx dz 1 A…

A: Topic  =Differential equation Correct option  = A

Q: If we are integrating by parts and we have u = x² and dv = cos xdx, what are du and v?

A: given u=x2 and dv=cosxdx

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: 14. Evaluate 4y dx +3ax dy, where C is the trapezoid with vertices (0,0), (2,0), (6,2) and (0,2).

A:

Q: 3) Find dy/dx Cas %3D X-

A: Given:

Q: 4- Find dy/dx for y = 3[(sin-(e-3x*)1² dy 3(sin-(e-3*)1* In3 2(sin-'(e-3**) 1(-6x) %3D dx V1- e-6x2

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Q: 3. Find dy, where; (x+y) = 2 a) cos (xy)- + e b) e+ iPtany=1 , u= xlax (use chain rule)

A:

Q: dx 2- Find dy of y = /cos-1(In (xy)) y %3D

A: Given: - The function is, y=cos-1(ln(xy))xy To find: - The derivative of the function, dxdy

Q: (у — сos-x)dx + cos x dy %3D 0

A: The given equation is y-cos2xdx+cosx dy=0 rewrite it as y-cos2x+cosx…

Q: 6. Find S(3y – y³) (1– y?)dy sin ycos y 7. Integrate: J sin² y dy 8. Find 3 S(5 - 3y-5)²dy

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Q: 1. Defermine the integrating thators of the pallo wing non- exnet exact esuations. A. (1+ 4xy -…

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Q: 4 cos x Let y = [, (2t + 1) (t + 8t)'/3 dt. Find dy/dx.

A: We will find out the required derivative for given function.

Q: 4- Find dy/dx for y = 3(sin-(e-3x²))2 dy 3[(sin-{(e-3*)i* In3 2(sin-1(e-3**) - 3x2 1(-6x) dx V1-…

A: Differentiate term by term

Q: dy/dx=x2+3y2/2xy

A:

Q: 3) [ - cos dydx X X In 8 In y 4) S S e**y dxdy

A: (3) we have to evaluate ∫π2π∫0x21xcosyxdydx let  u =yx ⇒dudy=ddyyx         =1xddyy=1x⇒du = 1xdy…

Q: (2e" sin(y) – 4y)dr + (–7x - e cos(3)dy = 0 not exact

A:

Q: 4- Find dy/dx for y = 3(sin-(e-3x*)2 dy 31(sin-(e-3*")r* In3 2(sin-'(e-3x")- dx 1(-6х) е 1 - e-6x2

A:

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.