1) Given x = Vu2 + E2 sin 0 cos 2 y = yu? + E² sin 0 sin 1 z = u cos 0 ds? = dx2 + dy2 + dz2 %3D where E is treated as constant Derive: u² + E² cos?0 ds2 du²+(u²+E² cos²»\ do² +(u²+E²) sin²v dx? %3D u? + E?

Q: 9.lf y = sin (4x – 5), then what is y'? O A. y' = - cos (4x – 5) O B. y' = - cos (4x) O c. y' = cos…

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Q: To obtain the General Solution of si What will be the form by separation of variables? cosv A)…

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Q: dy Find if y = In x5 + e-cos2x – In e?. dx dy 4 sin x cos x dy 5 es sin²x-cos2 x dx e cos2 x-sin? x…

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Q: Find the general solution of 2ey cos 2x dx + (ey sin 2x + 3y sec2 y2)dy = 0. a. e sin 2x +y tan y? =…

A: This question is related to differetial equations, We will solve it using given information.

Q: Find the particular solution : y" + y' + 16y = sin4x 1 (а) Ур — — 4sin4x (b) Ур 3sin4x --cos4x 1 (c)…

A: Correct option: C The detailed answer is listed below, kindly do like it if you find my answer is…

Q: If y = 12y sin(4z) – 12z sin(4y), then (z, y) = 6y? sin(4z) + 3z cos(4y) + h(x) O (z, y) = 6y²…

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Q: 2 sin? 11. y = 3x 2x2 12. y = cos°V2x – 1 3. 13. у %3D Vtan(х?)

A: As we know that; The chain rule: fgx'=f'gx·g'x The Quotient rule: fg'=f'·g-g'·fg2 The Power rule:…

Q: 21 40 JJJ. 7yz cos(10x5) dv, where E = sin (2) X = {(x, y, z) | 0 ≤ x ≤ 1,0 ≤ y ≤ x, x ≤ z ≤ 2x}

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Q: Show that an implicit solution of 2x sin2(y) dx – (x² + 11) cos(y) dy = 0 is given by In(x² + 11) +…

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Q: 2. Show that u(x, t) = cos(x – ct) is a solution of Ut + cuz = (0

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Q: Differentiate y = In (sin + cos ) cos -sin 2r Va(sin a + cos V") sin E + cos E 2r V(sin a + cos a)…

A: we will apply, chain rule: ddxf(g(x))=ddg(x)(f(g(x)))×ddx(g(x)) Sum rule:…

Q: Suppose tan u = %¾ (sm u>0) and tanuo12/5 Ccasx cO]. Ead he exsee velos OR the followly trgeronetnc…

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Q: 1) = sinx + ytanx dy dx 2) x = y + x sin? 3) Prove that (2xy – 9x2)dx + (2y + x² + 1)dy = 0 is…

A: 1   dydx=sinx+ytanx        the equation can be written as standard form        dydx-ytanx=sinx…

Q: Ou = 20 · x, du = 5 · sin(5· x) dx %3D Ou = 20 · x dx, du = cos(5 · x) Ou = 5 · x, dv = 20 · cos(x)…

A: we use the rule of integration of uv dx.see 2nd and 3rd step.

Q: The solution of the nonhomogeneous DE y" + y = sec?x is O None of these y = c1cosx + c2sinx +…

A: The given DE is, of the second-order and it is y''+y=sec2x which is non-homogeneous DE. So, first we…

Q: (a) If y = xV², then dy dx (b) If y = (2 + sin 3x)", then d (2 + sin 3x)" = T(2 + sin 3x)=-1(cos 3x)…

A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…

Q: Find dx ar and simplify the result whenever possible *+ sin2x sin' 5x 1. y = 2. y sin5x 3. y sin? 4x…

A: Given  The equation is y=-35cot5x3+cot3x3-3cotx3-x

Q: 1. If x - y = 25, then y" = c.) d.) - a.) b.) 2. If y = cos(3x+1), find y a.) 3 sin(3x+1) b.) -3…

A: Authoring guideline: As per the authoring guidelines, we can solve only the first three parts.…

Q: (3+ 7cos (x)) sin? (x) de 28. 29. sin° (9y) sec² (9y) dy / tan" (2) cos" (2) dz 30. [tan(2t) – sin°…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: What is the general solution of (sin 0 – = 0 ? 2rcos? 0) dr + rcose (2rsind + 1) do O sin 0 rcos e =…

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Q: a. Find the General and Particular solution of dy/dx = −8 sin 4x ; y = 6 when x = 0

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Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Evaluate ∫2x4x2-1dx          ...(1)

Q: 8 12. If y = then what is %? dx Vx+4' dy а. 4x(x + 4) dy С. dx = -4Vx + 8 %3D dx 3 dy b. dx -4(x +…

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Q: What is the trial particular solution for g (x) = (x² – 1) sin 2æ? O yp = (Az² – B) sin 2z Y, = (Ax?…

A: The trial particular integral for the 2nd order polynomial is: yp=Ax2+Bx+C The trial particular…

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

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Q: Match the following guess solutions yp for the method of undetermined coefficients with the…

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Q: Obtain the General Solution of: (z + 2)* cos yudz - [sin y In(3z 4 6) – d

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Q: The general solution of y" + 16y3 cost is: Select one: a. y= C, cos(4t) + C2 sin(4t) + 1 -tcost 15 O…

A: Using Solution of Linear Differential Equation

Q: Solve the problem: u – kuxx = e-t sin x , 0 0; satisfying the conditions u(0,t) = 2n, u(t, t) = 4n,…

A: Let the transformation ux,t=vx,t+Ax+B ...............(1)uxx=vxxut=vtthe problem ut-Kuxx=e-t sinx…

Q: What happens if you can write a function as a composite in differentways? Do you get the same…

A: 39. Part a). It is given that, y=cos u and u=6x+2 Therefore, dydu=-sin u  and  dudx=6 So,…

Q: If z = x2 – y2 and x t cos 2r and y = r sin t, then %3D a2z is ar2 (A) 2 cos (2r) + 2r? cos?(t) –…

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Q: Find the general solution of (cos cos y +ycos x ) dx + (sin sin x – x sin sin y ) dy = 0

A: The given differential equation is incorrect and hence the correct differential equation is as…

Q: 4) Differentiate each of the following: a) y = - cos²x c) f(0) = sin(20 — π) e) y = (52)²x g) y =…

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Q: 11. Evaluate * d²y dy - 2 + 5y = –17sin2x dx2 dx y = (C,e* + 68 |cos2x +(Cze* + 17 sin2x 15 y =…

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Q: 4. tanx dy + y3 sin? x dx %3D 0, whe х %3D0, у%3D 1 о у?(3- сos 2x) %3D2 о у (сos 2x - 2x) %3D 1 о…

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Q: sin ® 3y cos3ydy cos 3y dy

A: We have to find out the integral

Q: 4y" + 36 = csc 3x y- C, cos 3x + G, sin 3x +; (sin x - cos x) – 4x e y = C, cos 3x + Cz sin 3x - x…

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Q: d²y 10. dx2 -- 3y = 2e2* +10 sin 3x given that y (0) = 2 and y'(0) 4 dx %3D 29 Ans. 12 e2x +[cos…

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Q: 2. Test for exactness and find the complete solution of n dx + {In(2x – 2) + dy = 0 - (х-1)

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Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. @ y(x)…

A: We find the general solution of given DE  y"+y'=-cos(x)........(1)

Q: 1. Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); u = (i-)

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Q: fip Ify r' sin I, dx a)3x²+ cos x 3. O b) 3x sin x + x° cOS I O cos x 3x sin x + x³ COS 2 Od 13…

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Q: If u(x, y) = 2 tan-1 2 and v= In (x² + y?) , prove that: a2v = 0 дхду dx2

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Q: The general solution of y"+ 16y3cost is: Select one: а. y = C, cos(4t) + C, sin(4t) + tcost 15 b. y…

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Q: Show that an implicit solution of 2x sin?(y) dx - (x2 + 17) cos(y) dy = 0 is given by In(x? + 17) +…

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Q: 44. First verify by substitution that y (x) =x=1/2 cosx is one solution (for x > 0) of Bessel's…

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Q: 8. Which of the following is the solution of * [2x + ycos(xy)]dx + xcos(xy)dy = 0 x? + cos(xy) =c x?…

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Q: The general solution of y" + 16y = cost is: Select one: а. v = C,cos(4t) + C,sin(4t) + 1 -cost 15 b.…

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