given the general form x? + y + Dx + Ey + F = 0 (since it is a vertical parabol y term). x²+ х + y + = 0

Q: Use the method above to find a second independent solution of the equation ty" - y' + 4t³y = 0, t >…

A:

Q: snip

A: Except for degenerate cases, the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 defines an ellipse if ____.

Q: Consider the Euler equation ay"– (2a- 1)ay'+ (a +4)y 0, r> 0. Find conditions on a so that all…

A: In this question, we find the condition for the contact by using the given condition y tends to 0 as…

Q: dy 2х %3D (Зу + x)— dx

A:

Q: what is the annihilator for y=x e*cos 2x A D²-2D+5 B (D²-2D+5)² © D?+5 O (D²+5)²

A: We are asked to find the annihilator of the function.

Q: Q4: A particle is moving on the curve defined parametrically by the system of equation x = 1- 2cos?t…

A:

Q: ydx = x + Vy² – x² dy

A: Given that: ydx=x+y2-x2dy

Q: '4 I x1/2 dxi n = 8 (a) Approximate its value by using the Trapezoidal Rule.

A: Given: ∫04x dx where n=8 To find: The approximation using the following, a) Trapezoidal rule, b)…

Q: In the given Bernoulli's equation 6y²dx – x(2x³ + y)dy = 0, what is ƒ P,(y)dy?

A: I have appended the formula used in the solution part

Q: NOTE: Enter the exact answer. yz dx dz dy -180 J–120

A:

Q: y cos y dx dy dz x² +y° y -(7 +2/2 - 4) 16

A: Explanation of the answer is as follows

Q: By using the Lagrange method, find the general solution of P.D.E (x - y)p + (x + y)q = 2xz

A:

Q: If – 3x + xy – 4 = 0 then find dy da? at the point (-2, 1) in simplest form.

A:

Q: The position of a moving particle is given by s = t - 8t + 15, then its speed at t = 8 is

A:

Q: Calculate , e6x*+9y dx dy, where D is the interior of the ellipse () + ()< <1. (Use symbolic…

A: According to the given information, it is required to calculate the given integral.

Q: 11. dy _ xy+x² + y² ху+. dx

A: As per our guidelines we can solve only one question at a time. Please repost unsolved question…

Q: When written in cylindrical coordinates, the equation (x + y')2 = 1 is (a) r = 1. (c) r' cos'0 = 1.…

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Solve this equation: ди + a = at %3D u(0,t) = 0 %3D ди (L, t) = 0 az u(z,0) = 2 %3D

A:

Q: snip

A: To transform the equation Ax2+Bxy+Cy2+Dx+Ey+F=0,  B≠0 into one in x'and y' without an x'y'- term,…

Q: Q3- By using the Lagrange method, find the general solution of P.D.E (x - y)p+ (x+ y)q = 2xz.

A: Given: The partial differential equation is x-yp+x+yq=2xz

Q: Given [2r + y cos(ry)] dx +r cos(ry)dy 0. Show that the equation is exact and find its solution.

A:

Q: NOTE: Enter the exact answer. (36–z² xy dy dx dz

A:

Q: In the diagram below, given that XY 3cm, XZY = 30° and YZ = x, is it possible to solve for x using…

A: topic - trigonometric ratios

Q: 3x'y"+2xy' = 0 %3D

A:

Q: of Find and dy f(x.y) = /2x + 3y? df (Type an exact answer, using radicals as needed.) dx II

A: We can solve this as follows:

Q: Given that the DE y" (t)-6y' (t) + 6y(t) = 2e6t has a solution of the form Ce6t determine the value…

A:

Q: Utt = C°AU in IR3 Schve the equations welve %3D with initieh dotes U0)= ¢()ー 0 Ut(8っ0)= Y(R)=X

A: The partial differential equation given is as follows: utt=c2uxx The initial conditions given are as…

Q: $ x4* dx + 2x*y dy where C is the triangle wl vertices (0,0), (3=), and (2, 4) i ?

A:

Q: The cylindrical equation z = r2 represents which of the following? O a paraboloid O a semisphere O a…

A: The cylindrical equation z=r2

Q: dy sin(r-y). dr Q(3) Find the general solution of %3D

A: we have to solve the given differential equation

Q: 4x² + 4y² + 4z² dV = mz, where R is the solid hemisphere with z + y² + z² 0 Find the value of m

A:

Q: dx + 2xy = sin y , x(n) = 1 - dy

A:

Q: solve the differential equation with the given initial condition.

A: We separate the variables and then integrate both sides. C=integrating constant

Q: 4 du + 3, du -o is dassified as Jhe P.O E dx² © Hyperbotic Elliptic Parabolic there of

A: 4∂2u∂x2+3∂2u∂x∂y=0

Q: Find the cylindrical equation for (x-4)² + y² = 4². O a.r = 8 cos (theta) o b.r = 0 c. theta = 6.28…

A:

Q: Given the set of equations dx = y + sin y , y = (z – e²)? Which of the following is dx/dz? The…

A:

Q: Question I dy y - g", yw . -4 ky, ycu = %3D de

A: Given differential equation y'-y/x=xy^-1 , y(1)=-4 We will evaluate this as shown below

Q: 5. Given the Standard Equation the DE, Identify the roots * d²y d³ y dx³ dx² + dx - 2- m: 1+ √2,0…

A:

Q: Given the IVP 1+2xy + (y + x²)y' = 0 : a. Show that the DE is exact. fy = Ix = %3D b. Find the…

A:

Q: I keep getting different answers each time I attempt this question, so any help would be kindly…

A: We will find out the required volume.

Q: 10. Given that x d'y t°and y = e", where t is a parameter, dx2 %3D A. 9t e" 2. 3e C. 9et? D. 9e 1/3

A:

Q: Obtain the general solution unless otherwise instructed d²y 1. dr? - y = 10sin²x | dx2 SUMMARY OF…

A: Given differential equation, d2ydx2-y=10sin2(x) So corresponding homogeneous equation, d2ydx2-y=0

Q: Find the particular solution of (xcos? - y) dx + xdy = 0 ; where y and x = 1 - у %3D = - 4

A:

Q: 3. = 40e2x + 80 cos(2x) (D3 + 2D² – 16)y %3D |

A:

Q: Question 11 Find the solution, (D3+3D²+3D+1)y = 0 (A y = (c,+c,r+cx?)e= © y = c,e"+c,„xe -3«. Oy =…

A:

Q: A) Solve The Following Equation By (Lagrange Method): пр + ди = 2(x + y)u и %3D и (х, у) и дх ду и…

A: We’ll answer the first question since the exact one wasn’tspecified. Please submit a new question…

Q: Choose the values that would complete the general solution for y = arccos (-1 ±2tk HIN O O O O 0

A: Given:     y= arccos-1

Q: x?dx – /16 – x²(3y+y²) sin 2y = 0 - %3D

A:

Q: TT Find I = J? = Jó COs X dx 2 With trapezoidal method and n = 4

A: The integration can be approximated using the trapezoidal rule. The formula for the trapezoidal rule…

Q: By expanding (x – h)² + (y – k)² = r², we obtain x² – 2hx + h? + y² – 2ky + k² – r² = 0. When we…

A: