2 Given z = 2 cost + 30 and y= 5 sin t dt dy dt dy dx %3D %3D

Q: use Euler's Method to approximate the given value of y(t) with the time step h indicated. y(0.5); dy…

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Q: (ysinx + xycosx)dx + (xsinx + 1)dy = 0, with y(0) = 1 is %3D x*y? ++ = 9 3 3

A: Given that  The differential equation

Q: If x= sint and y = cost then 2 dx dy dt dt O 2 O -1 O 1 O O O None of these

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Q: integral f y^2 e^5y dy

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Q: eš [y – 3 (e* + 1 )²] dx + (ex + 1 ) dy = 0 dx/dy -x = sin 2y dy + ( 4y - 8y-3) x dx = 0

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Q: Use Euler's method with h = 0.25 to compute approximate value of y(1) for the IVP: (a) dy 1 = y sin…

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Q: Find the value of y(0.1) using fourth order Runge-Kutta's method from: dy =x+ y, y(0) 1. dx 1.11034…

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Q: t y = t dy Find dx 1 8t dy dx t dy Find dt dy dt + II II

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Q: 1.) +y=e+ dx=3e-t 2. .) d- given: x(0) = 0, y(0) = 1 dy-x=0 d+y=1 given a z (0) = -1, y(0) = 1.

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Q: Given I 2 cost +35 and y = 6 sin' t dx %3D dt dy dt dy dx ||

A: Given: x=2cos t+35y=6sin2t Therefore, dxdt=ddt2cos t+35       =-2sin  tdydt=ddt6sin2t       =6(2sin…

Q: at (x, y) = (1, 2) and z? = x2 + y² if dt dx = 4 and dt dy = 3. dt dz %3D %3D Find dz dt II

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Q: (1) d?y + 2y = 0 y(0) = 3; dy (at x = 0) = 2 dx? dp, dx d2v dy ....

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Q: 1. Solve for x(t) and y(t), given that x(0)=4 and y(0)=3 dy - y = 0 dx + x + 4y dt — 10%; х - | dt

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Q: da dy 3x? – 1 and dt Find at z = 1 if y = at x = -5. dt da dt

A: topic - derivative of a function

Q: dz evaluated at dt 4x If z=tan In with x=sec t and y=e". Then the value of y t= 0 is equal to ...…

A: Given,             z=tanln4x2y with x=sect and y=e2t.To find : The value of dzdt at t=0.

Q: dy -y ze°Cos(E) dt y le) =0 1+らine

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Q: siven z = 2 cost +26 and y = 2 sin?t %3D dt dy dt dy da

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Q: Given z = 2 cost +3 and y= 3 sin? t dx dt dy dt dy dx

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Q: Find the differential dy. y = ex/4 dy = (b) Evaluate dy for the given values of x and dx. x = 0, dx…

A: a) y= e^(x/4) dy= (1/4) e^(x/4)dx

Q: Given the IVP dy =x² – sin y, y(0)=.5 dx Estimate y(0.4) using 4th order RK method with step size…

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Q: Given z= 2 cost+6 and y= 5 sin t dz (i) dt dy (ii) dt dy (iii) da

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Q: By using method of elimination find x(1)+ y(1)=? for given: dx = 3x – y dt x(0)=1 & Recommended time…

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Q: 1. Solve for x(t) and y(t), given that x(0)=4 and y(0)=3 dy dx + x + 4y = 10; æ dt - y = 0 dt

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Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation…

A: We have given thatthe radius r and height h of a right circular cone are related to the cone’s…

Q: dy For = 9 + y and y(0) = 4, use Euler's method with h = 0.1 to approximate y(0.6). dx

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Q: use Euler’s Method to approximate the given value of y(t) with the time step h indicated. y(0.5);…

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Q: use Euler’s Method to approximate the given value of y(t) with the time step h indicated. y(3.3);…

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Q: Find the sloution of the given DE dy y-x dx y + x = Yexact y (0) = 1, h = 0.1 at x = 0.5 2 ? (find…

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Q: (a) Find the differential dy. y = eX/5 dy = 4 (b) Evaluate dy for the given values of x and dx. x =…

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Q: Given z = 2 cost +3 and y = 3 sin?t da dt dy dt dy da

A: Explanation and solutions is given below....

Q: Find the value of y(0.1) using fourth order Runge-Kutta's method from: dy =x+y, y(0)=1. dx 2.0

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Q: dy + 2 dy + y = sinh 3t – 5 cosh 3t ; y (0) = -2, y (0) = 5 II %3D |3D | dt? dt

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Q: 3 + 1)'0 dy calculate dx Given y = dt

A: From the fundamental theorem of calculus, ddx∫0xf(t)dt=f(x) And from the chain rule,…

Q: dw/ dt باستخدام قاعدة السلسلة ، فإن W=x? + y? X=cos t y=sin t = 0 = اللانهاية لا أحد من الآخر = 2…

A: Use differentiation

Q: f(x,y)=sinx+cosy+xy2, where x=cost,y=sint Find df/dt at t=π/2.

A: We can find the answer as below

Q: 4Calculate dy.dx. O 1-X y dxdy T メ T Sinx X. Siny.dy.dx- ydydx e Inx ☺ sS cany dady (* +y) ® xy dy…

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Q: Find the first three approximations using Euler’s method for theinitial value problem            y'…

A: Given   y' = 1 + y,         y(0) = 1, starting at x0 = 0  with dx = 0.1.

Q: Find the general solution for y(t) where; dy а. dt + 6t?y = 2t? dy b. + 10y = 0 dt

A: The given question has been solved in detail

Q: Given z = 2 cost +35 and y= 9 sin t da dt dy dt dy dx %3D %3D %3D

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Q: dy Find dt y = (t sin t)6 dy dt

A: Given: y=t sin (t)6 We have to find dydt: Consider, y=t sin(t)6=t6 sin6(t) To find dydt…

Q: Find the sloution of the given DE dy y-x dx y + x = Yexact - y(0) = 1, h = 0.1 at x = 0.5 ? (find…

A: Introduction: Euler's method is a tool that is used to solve an initial value problem numerically.…

Q: Given x = 2 cost +33 and y=8 sin t |3D da dt dy dt dy dx

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Q: "ind general solution for dy dy + 3 + 2y = -20 sin 2t, y (0) = 2, y' (0) = 1. dt2 dt

A: Ode

Q: dy !z = 3e*jSg y = 3z² + sin(z) GS I3I %D dx dy dy dz dx dz'dx

A: Given: z=3ex, y=3z2+sinz To evaluate: dydx=dydz⋅dzdx We know that, ddxex=ex, ddxxn= nxn-1, ddxsinz=…

Q: use Euler’s Method to approximate the given value of y(t) with the time step h indicated. y(2);…

A: Here we solve the given function by using the Eular’s method:

Q: tions y(0) = x(0) = 0: %3D dx 2 -y+x+ = 5 sin t; dt +x-y+ 25 dt dy dx = et 3 dt dt 12

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Q: dy x2 + y2 if dx Find at (x, y) = (5, 6) and z? dz dt = 9 and = 7. dt dt dz dt Additional Materials

A: To determine the derivative.

Q: Given dy =x +y with y(0) = 1 %3D dx Determine the value of y when x = 0.1, with step size h = 0.05…

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Q: · y" – 2y' + y = t² +4 + 2 sin t, y(0) = 1, y (0) = 3, yp(t) = t² +4t + 10+ cost

A: We will find out the required solution.

Q: dy = t Vy – 3 dt

A: According to our company policy, I am supposed to answer only one question at a time. For the rest…

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.