a) f(t) = t² + 6t – 3 - 3 b) f(t) = e'sen ht

Q: Solve the follow ing initial value problem: 3x(t2- 1)dt+ (t³ + 8x- 3t)dx= 0, t(0)= 1

A:

Q: The separable equation dy/dx=xy2 admits a constant solution equal to (x)=0. Is it True or False?

A:

Q: Solve the IVP -8 0] *-[× -16 dx dt x(t) = x, x(0) [8]

A:

Q: 1. Show that if you differentiate both sides of x2 + 2y³ = 6, the result is 2x + 6y2 = 0. Then solve…

A:

Q: Solve the differendialegimaition: (2x+e)dx + (xay co

A: Make some simplification and rearrange the given differential in exact form.

Q: 1. If z = 2xy – 3x²y and x is increasing at 2 cm/sec determine at what rate y must be changing in…

A: Z is neither increasing nor decreasing at the given instant. A function is said to be neither…

Q: 2. a) Use the Trapezoid Rule to estimate the value of: [V10-7e-03x dx. Letn=6. x |f (x) Round each f…

A: The equation for calculating the integral of a function y=f(x) by trapezoidal rule is; I=∫x0xny…

Q: 3. Find for the simplified general solution of (1 + x³)dy - x²ydx = 0

A:

Q: --——-^*[e'-In(2t+1)]dt, find g'(x) . dx 4 A e*+ (2x + 1)² 4 B et + (2x + 1)² 2 (C) e*- - (2x + 1)²…

A:

Q: Q4/ 1- Evaluate: f/2fy sinx dy dx ди 2- If u = x² + ey² ,x= sin 2t , y = cost² find at

A:

Q: solve the differenhal equa hon by varianon of parameters y" + 3y't 2y 7 te* y (x)

A:

Q: If x2y3 = 4/27 and dy/dt = 1/2, then what is dx/dt when x = 2?

A: Given:

Q: d & fle²- · *[e' – In(2t+1)]dt, find g''(x) . dx -2 If g(x) = - A B c) e*- D 4 et + (2x + 1)² e* -…

A: The Leibnitz rule for differentiation under integral sign is,…

Q: Find the solution and the interval of existence for: (1-x2)dy/dx + 2y = (1-x)2

A:

Q: If f(x, y) = 3x² – 7y, then the total differential of ƒ at x = 1 and y = -2 is :

A: we need to find the total differential of the function  f(x,y) = 3x2 - 7y2 the total differential,…

Q: Solve the initial value problem given by y' = (x2 + 2y2)/(xy) ,  y(1) = 1 What is the interval of…

A:

Q: Solve the initial value problems for y as a functionof x. (x2 + 4) dy/dx = 3, y(2) = 0

A: Given Data : Differential Equation x2+4dydx=3, y2=0                      1 The given initial value…

Q: Solve the initial value problems for x as a functionof t. (3t4 + 4t2 + 1) dx/dt = 2√3, x(1) = -π√3/4

A: dxdt(3t4+4t2+1)=23=>dx=23dt3t4+4t2+1=>dx=23dt(t2+1)(3t2+1)=>dx=23…

Q: solve the differential eq + 2x) dx = = (2y \1+x²y² |dy 1+x²y²

A: The given differential equation is: y1+x2y2+2xdx=2y-x1+x2y2dy

Q: یک 2. G(x) = L tanz et et +3 -dt

A:

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

A:

Q: 2. gxc2x2+3 dx Selast & du 니 get x in terms of u ut 2x2 +3 4-3 = ㄹ x² 4-3 x = 이들 4-3 z soke har x…

A: Given ∫x2x2+34dx

Q: Solve the DEQ given the initial condition (2,0). Graph it on the slope field. 11 « 10 Let…

A: dydx=g(x,y)g(x,y)=ey(3x2) - dydx=ey3x2Separating the…

Q: 33 2Vx- f(x) = T sin sin 2x + Ve2x + 2x – In e, x + 1 - 1-x (1–3t)5(t³-8) alt) t # 2

A:

Q: cos (2t + ) dt e21-3 -3 e 4 64e3 7 e-3 4 7 e3 4

A:

Q: Find the solution and the interval of existence for  (1-x2)dy/dx +2y = (1-x)2

A: The objective is to find the solution and existence for  1-x2dydx+2y=1-x2dydx+21-x2y=1-x1+x The…

Q: Q4) Use the chain rule to express dy /dx in terms of x and y t2 y = t2+1 and t = 3x3 – 3 where x =1

A: Given y=t2t2+1 and t=3x3-3 and x=1

Q: 1. e-st cosh t dt 2x +4 2. 2x2 + 21x + 34

A:

Q: 1/4 sec2(t) dt J-x/4

A: Given: I=∫-π4π4sec2tdt

Q: (x² + 4) dy 山 3. y(2) = 0

A: we know that ∫dxx2+a2=1atan-1xa+C,  where a>0 see below the answer and calculation

Q: sin(2t + ) dt e21-3 4 7 4 4 64e 7

A:

Q: find the general solution of dy/dx + (3/x)y=2/x^2 as a function of x

A: Given,           dydx+3xy=2x2

Q: -7x f(x, y) = e" sin(4x + 5y) af e^(-7x)(4cos(4x+5y))-7sin(4x+5y) af 5e^(-7x)cos(4x+5y) dy ||

A: Partially differentiate with respect to x and y by using product rule.

Q: Solve the differnetial equation: dy/dx=3/x^2-3x^2+2 with the initial conditions (1,8). show work

A: By using variable separable method we can calculate the given differential equation. See attached…

Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: Can i get help step by step please

A:

Q: The approximation of I = f(x-3)** dx by composite Trapezoidal rule with n=4 is:

A:

Q: -2 2 dx dt -12 8 with the initial value -2 x(0) = -5 x(t) =

A:

Q: Solve the initial value problem by using integration. g' (x) = , 9 (1) = 4 x+1 %3D

A:

Q: Solve integration by (udv) T/2 DS Š X cos(x) dx 2) { X cos (ux) dx 7/2

A:

Q: 5. Find the General and Particular solution of 2 = 3y ; y = 3, when x = 0 dy dx

A: We have dydx=3y Now, we can write this as: dyy=3dx Now, integrate both sides: ∫dyy=∫3dx⇒lny=3x+C…

Q: b) Find if dx2 d²y Lm Vt2 + 5 dt + sinx = y – x secx rsinx

A: We will first find the first order derivatives using Newton-Leibnitiz theorem. The , we will find…

Q: 3 9 dx dt -1 -3 with x(0) 4 Give your solution in real form. X1 = X2 = ||

A:

Q: In(|(2 +1)"(z + 3)|l) 15x - 13 dx = X (Don't forget to include the constant of 2-2x 3…

A: topic - indefinite integral

Q: Solve the initial-value problem for yy as a function of xx. (64−x2)dydx=1,y(0)=5(64-x2)dydx=1,y(0)=5

A: (64-x2)dydx=1⇒dy=dx64-x2integrating,                ∫dy=∫dx64-x2+c      [c=…

Q: d rIn(x) t tan(t) dt|. dx -1

A: we have to evaluate the following

Q: 3. Integrate! 12e-0.21 а) -dt b) 6r 3,2 Se041 dr dx c) f- x. V1+ In 3x?

A:

Q: Q1: Use Newton - Raphson method to estimate the 3 Yoot of fcx) = x-X-1, employing an initial guess…

A: We have to use Newton-Raphson method which is widely used in finding the root of nonlinear…

Q: ne differential ay of 'uonpuni y = V 5 - x2

A: