t -4t +24 - Jydt = e s(t-3) yro) = 0 ,y'co)= o ,y'c0) = 0

Q: cos (2t + ) dt e21–3 %3D 4 -3 4 64e3 7.

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Q: Find the differential dy: y = In (sec² (3ª²–2x+5)).

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Q: dx =- 1. dt dy at x = 2 if y = 4x° – 2 and dt %3D Find - dy dt

A: Given: y=4x2-2 and dxdt=-1 To find: dydt, when x=2.

Q: Obtain the particular solution satisfying the initial condition indicated. (variable separable) dx…

A: Use the variable separable method and satisfy the initial condition. Also use the properties of…

Q: dy dz Find at z = 1 if y = 4z +4 and = 2. dt

A: Given: y=4x2+4

Q: y, thên thế total differential of and y O df = 11 dr + 16 dy O df = 15 dr + 19 dy O df = 12 dr +18…

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Q: dw where w = cos 8x sin 3y, x=- dt 5. and y=t". Use the Chain Rule to find 2

A:

Q: Let y = tan(5z + 6). Find the differential dy when a = 4 and dæ 0.1 %3D Find the differential dy…

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Q: Find the location and velocity at t = 4 of a particle whose path satisfies dt dr (3t-1/2, 5, 8t) and…

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Q: d3x 2. Verify that sin kt is a solution of the equation in + k3x = 0 %3D dt3

A: Explanation of the answer is as follows

Q: d y dy 14. dt2 +2, + y= 2 cos 2t dt У (0) —D у (0) — 0

A:

Q: Solve the following initial value problems using Laplace Transforms:

A: a.) The given initial value problem is,

Q: Use the differential dy to approximate Ay when x changes from x = -3 tox = -2.99. y = x2 + 1 Enter…

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Q: Y' + 3Y = 6e-3t cos6t + 24 ; Y(0) = 0,

A: The given IVP is as follows. Y'+3Y=6e-3tcos 6t+24, Y0=0 Apply Laplace transform on both sides of the…

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: A particle moves on the circle x2+y2=25 in the xy-plane for time t≥0. At the time when the particle…

A:

Q: find dy>dt.…

A: Given function, y=ecos2pt−1

Q: Consider the direction field of the differential equation dy/dx=xy-8)- 7-9. y 7 YND but do not use…

A: Given dydx=x(y-8)2-6 We know that slope of linear equation id the it's derivative So, m=dydx

Q: (b) Solve the integral [(3x– y)dx+(2x+3y)dy along the curve x = y³ from (0,0) to (1, 1).

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Q: The solution of the differential equation using dy + 6y = 7e-3t is dt Laplace transform „given that…

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Q: 13. dy/dt = y²(1-y)², -∞ <yo <∞

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Q: - d² y dt² y (0) = 10 dy 4 - 5y = e-3t sin(4t); y (0) = 3, dt

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Q: Find the singular sol" of the differential eqh (P+1)² (y-px) = 1 -

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Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

A:

Q: The two functions x(t) and y(t) satisfy the simultaneous equations dx/dt - 2y = -sin(t), dy/dt + 2x…

A: Given: dx/dt - 2y = -sin(t), dy/dt + 2x = 5cos(t)

Q: B- The velocity of a particle v (msec-¹) at time t(sec) satisfies the differential dv equation…

A: We have given differential equation  tdvdt=v+t dvdt=vt+tt dvdt-vt=1 Comparing this with differential…

Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: The solution of the differential equation using Laplace transform y +16y 0; y (0)=6, y(0)=4.…

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Q: Find dy/dt. 13) y - cos (πt - 19) 14) y = 4t(5t + 2)4

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Q: dw where w = cos 8x sin 4y, x = dt and y =t". 4 Use the Chain Rule to find

A:

Q: Let z(x, y) = 2x2 3y2 where x = 2s – 4t & y = 9s + 8t. | dx dy ду az Calculate ds dz & and using the…

A: We have to find all first order partial derivatives.

Q: Solve from t 0 to 3 with h = 0.1 using Euler's method, dy = y sin t, y(0) = 1 dt

A: Given: Differential Equation To Find: y(3)  Fomulae Used: The Euler's method states that  yn+1 = yn…

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

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Q: dz az B. Find əx and ay 3. x eY+ cos xy36xz+5x²

A: partial derivative

Q: dW Find at t=0, if dt .3, W = x*y+ zxy whe x = sin2t, y = cos ?

A:

Q: Find the solution of the differential equatlor dy 3xeY, y(0) = 0 dx %3D

A: Consider the equation

Q: Suppose w = In(8x² + 2y² + 3z²) , x = 9 cos(t) , y = 9 sin(t) , and z = 8/t. Compute dw/dt in two…

A: To find: The derivative of w and the value of dwdtt=8  Given: Suppose w=ln8x2+2y2+3z2, x=9cost,…

Q: Find dy if y = In* +1 7 -t dy dt

A: Derivative is below

Q: 5.Express this model of an electric circuit d²y dt² dt As a pair of first order equation +6+5y=sin…

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Q: 1-fd dydx R = {0,1} * {2,5} y2 2-S y2 (1–5x)2 dxdy R = {0,1} * {0,2}

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Q: Solve the differential equation using Laplace transformation y" – 2y' + 3y = 2t²e3t where y'(0) =…

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Q: Show that a particle, located at the origin at t = 1 and moving along the x-axis with velocity v(t)…

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Q: 5.Express this model of an electric circuit d²y dy +6 +5y = sin10t, y(0)=0, y'(0)=1 dt² dt As a pair…

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Q: (a) Consider the direction field of the differential equation dy/dx = x(y – 8)2 - 4, but do not use…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Q2) Use the chain Rule to find dw\dt of y w = =+2,x = cos²(t), y = sin² (t), z =, at t = 3

A: In this question,w is function of x,y,z and x,y,z are the function of t so first we find out…

Q: What is the differential equation of the orthogonal trajectories of the family of curves X2 -…

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Q: By (d) dy 2- = 3t + 2, y(0) = y'(0) = 0. dt By +4 dy + 20y = -3 sin 2t, y(0) = y'(0) = 0. (e) dr² dt…

A:

Q: 5.Express this model of an electric circuit d² y dy +6¹ +5y=sin10t, y(0)= 0, y'(0) = 1 dt² dt As a…

A: First I have introduced two functions and then find pair of first order differential to the given…

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.