(t + 25)y' + 2ty =t°(t² +25). %3D

Q: d'y & dx Find d'x to the : dy *yーy=7 %3D7

A: We have the expression x2y2-y=7. Differentiating both sides of this equation with respect to x, we…

Q: find dy/dx

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Q: N3xy -y,whtre x sint and y =e. find dwl dt whin

A: w=x2y-y2x=sin ty=et

Q: dy Differentiate parametrically to find dx in terms of t: x = 4t?,y= 2t3

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Q: Q.1B) Solve the follwing diferential equation: 1 dy x dx siny + ycosy 2logx +1

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Q: d"y Q5 dx * - 5 d³y +74 – 3y = 20 sin(x), y(0) = - 1, y'(0) = 2, dx use the method of Variation of…

A: This is 3rd order first degree non homogeneous ordinary differential equation.

Q: Q! Salve! y? -y?+2y=Sin3× using D-opevtor Method

A: The given differential equation is: y'''-y''+2y=sin(3x)

Q: dy given that In(x + y2)-tan-1 31) Find = 0. dx

A: Given: lnx2+y2-tan-1yx=0 To Find: dydx=?

Q: dy from the equation vx + y = 1 + x'y² dx Evaluate when x =1

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Q: y = sin²(2x) + %3D et dy Find Y dx Inx

A: We have to find solution

Q: dy Find the value of at t = 1 if dx? Vt2 + t, y = t2 + 3 x = 4

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Q: dx 4.Exaluate I=| correct to three decimal places by Trapezoidal rule with h=0-25.

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Q: d'y Calculate y = eX + e* dy %3D dx2

A: It is known that if  we have a function f(ax) then the derivative of the function is,   Here it is…

Q: dy Q3) If y = In[sec 0 + tan 0) find- dx

A: To find dy/d(theta)

Q: y = sin (2x) + et ,Find dy Inx dx

A: 1. Differentiation can be defined as a derivative of a function with respect to an independent…

Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

Q: secx Q1.a) Find 2 if y + SE dt = xy dx sint+1

A: Simply take the derivative with respect to x as shown below.

Q: Get general equation of this DE: (1 + y^2)dx + (x^2y + y + 2xy)dy = 0

A: Solving the DE by seperation of variables

Q: Exercise 1. find the differential dy (la) y = 3z? (1b) Find y = V9 - z2

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Q: rt%3Dr/6 t cos(2t) dt t=D0

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Q: y = sinx from x = = to x = n and the x axis 2

A: The required solution is:

Q: (4-y)dx +dy =O what is the of differantial general soluttion equation ?

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Q: dy sin(4x) Find for y dz V1 - x4 dy de

A: The given expression is y=sin(4x)1-x4. Find the derivative of the expression. The quotient rule of…

Q: dx 6 when x=1, what is dt dy If y=x is expressed with parametric equations such that dt

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Q: dy where y = coS cos (V5æ). Find dx

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Q: Cos° x dx3D J7/6 Vsin x

A: Given that: ∫π/6π/3cos3xsinxdx

Q: Differentiate parametrically to find X 1 t-1 y=t³+2 dy dx in terms of t:

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Q: dy - f *P, = 7 dt y(0) = 4.

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Q: Given a = 2 cost+35 and y =7sin t %3D dx dt dy dt |3|

A: Topic : differentiation

Q: dy Q2) Find by using Chain Rule for y = sin34t dt

A: dy/dt for y= sin34t

Q: cos(t)y'-tsin(t) = y ; is this seperable or non-seperable?

A: It can be shows that it is not separable. See the next step

Q: Find 4 at the point t = 5. dy dx c(t) = (t^, t³ – 3) dy dx (at t = 5) = ||

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Q: dy Differentiate parametrically to find dx in terms of t: 1 y = 2t2 + 4 X = |

A: x = 1/(t-1) y = 2t2 + 4 We have to find dy/dx

Q: dy Find xp. y = tan -1( In 2x°) %3D dy xp

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Q: 3e2º sec 20 dy determine de Given y = V(0-2)

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Q: dy Find at the origin on the curve: - dx x² + y + x + 3y 0

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Q: Chose only two: dy 1. Find for y + In x2 y2 -cos 2x* = 27 dx 2x+1 2. Evaluate: f dx -4

A: We use chain rule and product rule while differentiating the given equation.  Also for integration,…

Q: dy 4 Find for y dx V10 – x?

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Q: Find the 2nd solution using variation of parameter. y" + 16y=0; y₁ = cos4x For the toolbar, press…

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Q: dy given that y= Vx² (x – 4) dx la) Find %3D

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Q: ds where t+s = 2s . dt Find %3D 6.

A: t+s=2s

Q: cos y f(x, у, z) -D xz2 XZ

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Q: Find dy/dx. - tsin(t), y = t² + 5t %3D %3D

A: givenx=tsinty=t2+5tfirst we differentiate these two then we evaluate dydtdxdt which is equal to dydx

Q: Q2) Evaluate , S2 xsiny? dy dx 0 Jx2

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Q: dy Find -5 y%3D(2+cos4t) dy dt

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Q: Find dy/dx if y = J' V1 + ² dt. Explain the main steps in your calculation.

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Q: d. Try to find dx dy at (0, 0) on both graphs. What goes wrong? How does this relate to their…

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Q: dy Differentiate parametrically to find dx in terms of t: %3t2, y3 6t

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Q: dy Find where y = sec-' (V3x³). dx

A: