Using v = ln u and v = f(x) + g (y), show that the solution of the Cauchy problem is y²u² + x²u² = (xyu)², u(x,0) = et² * ( 2² +²3²). i- u (x, y) = exp

Q: If g(t) = (√t 4) (√t + 1), then: g'(4) =

A:

Q: Calculate r' (t) and T(t), where r(t) = (6 +5t,9 – 61, 2t). r' (t) = ( ). T(t) = ( ).

A:

Q: Use Exact, Then solve (1 = In(x) +)) = (1 – In(x))y`

A:

Q: Find the general solution of dy + y cot(x) = 6 csc'(x). dx

A:

Q: Show that P2(x) = f(a) + f'(a)(x − a) + c2(x − a)2 for each value of c2 satisfies the requirements…

A:

Q: 9. Given an infinite collection An, n=1,2,... of intervals of the real line, their intersection is…

A: Let An : = [ n ,∞)  where  n = 1,2, 3 .....  . So { An } n∈ℕ is an example of infinite collection…

Q: The y, of y'"-y=2x2-x -3 by using variation of parameters is: .A Y,(x)= x - 1 .B y,(x)=x² + x +1 .C…

A:

Q: Solve the following equation by using separation variable method: u(0,t)= u(6,t)=u(x,0)=0 u, (x,0)=…

A:

Q: 1 dy y = x-'(a² + x²)z, solve for dx

A: Solve for the derivative

Q: poin If g(u) —D V9u + 3 then g' (u) =

A:

Q: The general solution of x' = 2x + 5y and y' = -2x - 4y

A:

Q: Let h(x) = f(x) %3D where f (x) = In(3x² + 2x + 2) and g(x) = -2x. What is h' (x)? g(x)' Select the…

A: We have to find the derivative of h(x).

Q: Solve min udr, subject to u(0) = 0, u(1) = 1, ur'dr = c %3D =C.

A:

Q: For y = f(x)=3x-1, x = 5, and Ax = 3 find a) Ay for the given x and Ax values, b) dy = f'(x)dx, c)…

A: Results:(i) If y=f(x) ,then (i) If y=f(x) ,then

Q: Find a solution of x dy = y²-y that passes through the indicated points. dx (a) (0, 1) y = (b) y = 1…

A:

Q: a) If L-{F(s)} = f(t) and L-1{G(s)} = g(t), and if a and B are constants, then L-1{aF(s) + BG(s)} =…

A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s). That is; f(t)=L-1[F(s)]

Q: 2- Solve the following equation: Utt = c?uxx +, u(0, t) = u(2, t) = 0 u(x,0) = x? ,u; (x, 0) = e*

A:

Q: find all functions u(t) that solve the equation u'(t)+t*u(t)=-t * e^(-t^2), subject to u(0) = 1

A: Linear Diffrential Equations: The ordinary linear differential equations of the first order are…

Q: Let f(u) = u* and g(x) =u = 2x* + 6. Find (fo g)'(- 1). (fo g)'(-1)= (Туре an exact answer.)

A: Given:- Let f(u) = u4 and g(x) = u = 2x4 + 6   To Find (fog)'(-1).

Q: 1 Find h' (u). Show your work. Let h(u) = 4u³ – - u?

A:

Q: Write the system x'= e"x – 4ty+9 sin(t), y' = 7 tan(t)y + 9x – 4 cos(t) in the form = P(t) + F(t).…

A:

Q: а.) Solve x' = -5] x+ -2 [sec t] x(0) 1 b.) Solve x' = x + x(0) 1 -2 U5

A:

Q: min z = 2x1 + 3x2 + 4x3 s.t. Xx1-x2 + x3 10 x12x2 + 3x3 ≥ 6 3x14x2 + 5x3 ≥ 15 X1, X2, X30

A:

Q: Solve the IVP: X' = AX, where --() 3 1 0 2 -1 0 0 A = 3 and X(0) = -1 2

A:

Q: f(x, y) = e-7x sin(2x + 5y) of gl& дх af ду || 000 ---

A:

Q: The function y1=ln x is a solution of xy''+y'=0 A) Find a second solution y2 on the interval…

A:

Q: g Solve Rour of the following D.E A)(xュ)dx + 2xy dy dy B) ャリ=ex c) (xx v y'es )dx -(y- )dy zo D) (X…

A:

Q: (b) If f (2) = (249 + 8) e8ɛ, then at how many points the function f (2)is not differentiable? (c)…

A:

Q: find dy/dx x(х+1)(х- 2) (х*+1)(2х+3) 25) у%3 43) у%3D 1+(lin x)? 1+(ln x)?

A:

Q: b) y = cos(5x) ln(x² + 1).

A:

Q: Salve 6y"o)-5y'Lx)+Yx)= esinx+ cos2X with

A: