Q3: Solve the equations sinh 3x a) S 4+2 cosh 3x 3 sinh 5x dy find dx b) If y = 4x2 c) 5 cosh x +3 sinh x = 4

Q: Find the value df (a) that Make ECX) is Contincity at X- Ž

A: Given that :f(x)=cosx2x-π      ,             x≠012a2-3a+4      ,   x=0

Q: 2 y = 0.38 sin x-.49x²

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Q: 2. x COs2x dx w hat is the value of integral 3.

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Q: Solve using Euler's Method dy dx sin(x+y) ex,y (0)-4, h-0.1 -

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Q: Q5: Solve by using Modified Euler's Method. dy = x + cos(y) ;0 <x<1 ;y(0) = 1;h = 0.5 dx

A: Given the DE is dydx=x+cosy,0≤x≤1,y0=1,h=0.5. The modified Euelr's method is defined as follows:…

Q: 9. If y = sinh 4t and r = sinh t, show that 2 dy (a) (1+2²) = 16(y? +1), dr dy (b) (1+x²)- dx2 dy…

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Q: find tu general Solution of: 2x a) y"-y' - 6y + Cosh = e b) y! -Y = Cosh 2x + Sinh x

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Q: 2FI 2 sin nx dx cos nx dx =0, where n integer. %3D !! 0.

A: Note: -     as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: B: By using Homogenous method solve the first order differentia еquation (1+ e») dx - e"l> -1) dy =…

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Q: Q5: Solve by using Modified Euler's Method. dy = x + cos(y) ; 0 < x <1 ;y(0) = 1 ; h = 0.5 dx

A: Disclaimer: We use the modified Euler's method to solve a first-order ODE and find the value of the…

Q: Obtain the General Solution : • tan'ydy : sin xdx e • COS "x sinx dx o • (3t sinix) dx = sin 4x dy

A: Solve above differential equations.

Q: 3. Find a result by using exact for a. cos(x + y) dx + (3y2 + 2y + cos(x + y))dy = 0 2)dx

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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: 2 1 æ sec-(x) dx 2/V3

A: By see this solution below

Q: If y = (4x) sin ( 3z) then %3D dy dx (Be sure to express your answer in terms of x)

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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: pol DA 4. x dy + y dx = 0 (3x²y² + 2y³ - 4y) dx + (2x³y + 6xy² - 4x) dy = 0

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Q: . Evaluate using integration by parts 8. (5x - 3) sin(12x)dx = TC 6.

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Q: Solve dy りー! り(-)ニ。 dx ス+3 © xy! =1+X

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Q: 1. Obtain the General Solution. Use reduction to exact. Simplify your fin y(y + 2x- 2) dx - 2(x +…

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Q: 2. у(у+ 2х — 2)dx — 2(х + y)dy 3D 0

A: A differential equation of the form M(x,y)dx+N(x,y)dy=0 is said to be exact iff, ∂M∂y=∂N∂x

Q: Show that if you differentiate both sides of x 2 + 2y 3 = 6, the result is 2x + 6y2 (dy/dx)= 0. Then…

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Q: 1od of undc cients, obtain the general y" – 2y' – 3y = 2 sinx

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Q: Simplify (if necessary) then Compute: y" +y' for [6(cosh2x- sinh2x)] d -3x2 dx a2 y(z) = [; (z²x+…

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Q: In Exercises 28-34, find ƒx , ƒy , and ƒz .

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Q: 2. if 2x3 +10 x?siny-y"tanx = 0 ノ the y' so dy write ex pressin in terms of X and y.

A: Applying implicit derivative we have

Q: ſe^(3-z) sin(2+z) dz *

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Q: show that the differential eguation is exact, then solre that method using 2 2 dy- x²-x+y? |

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Q: Q2. Solve x = cosx for solution exact to 3D by Newton's method (with xo = 0) and bisection method…

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Q: In? (In(ax)) dx,a >0 -dr, a a. 2x In(ax)

A: You can solve this problem using the substitution method

Q: When two particles start at the origin with velocities v(t)=cost and u(t)=sin2t, how many times in…

A: We set the equations equal and solve for t

Q: KIN KIN 0 2 d2 sinr do dr dọ

A: A detailed solution is given below.

Q: Apply Newton's Method using the given initial guess. (If an answer does not exist, enter DNE.) y =…

A: The given function is y=2x3-6x2+6x-1, x1=1 find the derivative of y  y'=6x2-12x+6, x1=1

Q: Q2// Use Euler's method (with all details) to find approximate value of y when x = 3 of = 2y-2x²-3,…

A: The Given initial value problem is: dydx=2y-2x2-3, y(0)=2, h=0.3 To find: y(3) using Euler's…

Q: Evaluate the exact value of the multiple integral. 3z (2y 24 sin(2x) dx dy dz -y

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Q: II. Solve th following DEs by LT. 1. y" + 2y' – 3y = sin(2x), y(0) = y'(0) = 0 %3D -

A: We are given a linear second order nonhomogeneous differential equation with constant coefficients…

Q: (3x + 2y3) dx + 3xy2 dy = 0 ,  y(1) = 1

A: Given: (3x + 2y3) dx + 3xy2 dy = 0 ,  y(1) = 1

Q: 2. Solve for general solution using exact method. (cos x cosy – cotx) dx – sinx siny dy = 0 %3D

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Q: 2. Use trigonometric substitution to Vx² – 25 dx integrate: 4

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Q: (2x sinh2 + 3y cosh?) dx – 3x cosh dy = 0 |

A: Concept Used: For  y'=f(x, y)   ...(*)If f(hx, hy)=hn f(x, y)Then (*) is homogenous equation of…

Q: (g) y = Vtanh 3r (h) y= sinh(cosh 2.x)

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Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the…

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

Q: Q4. Test for exactness and solve (ycosx – cosy)dx + (sinx + xsiny)dy = 0

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Q: 2. Solve (sin y – 3x² + 5)dx + (y +x cos y)dy = 0. (Test for exactness and solve)

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Q: Use Euler's method (with all details) to find approximate value of = 2y - 2x² -3, given that y = 2…

A: Given: y'=2y-2x2-3 , y(0)=2 , h=0.3. We find y(3) by using Euler's method. The formula for Euler's…

Q: 4. Solve for general solution using Exact method. Show test for exactness x²y dx + (1+ x³)dy = 0

A: Given differential equation is not exact, we need to multiply something to become exact as follows.

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: let's consider the equation (2xy - sec2 x) dx + (x2 + 2y) dy = 0

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Q: on the right. Prompts Submitted Answers D Ssin(3x)sin(4x)dx S(cos(x) - cos(7x)dx} Jsin(3x)cos(4x)dx…

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