K is the midpoint of JL J K If: JK = 5x +1 and %3D KL = 7x 3 - Find JL.

Q: b) Change the order of integration for . S(x- Jy=o Jx3xy) dxdy then evaluate it. |

A:

Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: xy dx (x² + 3y) dy = 0 -

A:

Q: Find the integrating factor for the First order leaner DE- x² ay +4xy=2x³e¬*? dx e 2x2 e 4x or

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Q: JK = 4x + 8, %3D KL = 5x + 6, and JL = 86, %3D Find KL. J K L

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Q: The special integrating factor of y'dx+(3xy + y² -1dy = 0 is: a. e3y b. Зу С. У d. y-3

A: Solution

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation to the indicated value. y' =…

A: To solve the given differential equation by Runge kutta Method of order 4 first we fill find the…

Q: Find r(t) that satisfies the initial condition(s).…

A: Given: r(0)=2i

Q: Given: J, (1 + 2x) e¯* dx. Using integration by parts and letting u = -1 – 2x, dv = ;ƒ(x)dx, then…

A:

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value.…

A:

Q: Given : 6x³e** +3 dx. Using integration by parts (S udv = uv - f vdu) and letting u = f(x), dv =…

A: Given,           ∫6x3ex2+3dx

Q: Given : S 6x³e**3 dx. Using integration by parts (S udv = uv – dv = 3g(x)dx find h(x) if ſ vdu =…

A: Let's find.

Q: 3. (x³+xy²-y)dx + (y³+x²y+x)dy =0

A: We need to find the solution for (x3+xy2-y)dx+(y3+x2y+x)dy=0

Q: dz Find- at t = n, if x=21sin' 12t + 170, z=19cos12t +190t . %D dx

A: The value of sin (npi) = 0 We will put t=pi in dz/dx

Q: Obtain ∫C  ez / (z - πi) dz with C defined as z(t) = 4eit and 0 ≤ t ≤ 2π

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Q: Find the forocings: of 3t rt +4 t+t dt. dx x'(x-1).

A:

Q: SSS 12z dV E where E is enclosed by z = x? + y² and z = 1 О Зл O 27 O 4T O JT

A:

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value. у'3D…

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Q: dx + хydy %3D

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Q: Calculate the “n” of the DE with the given 6y^2dx-x(2x^3+y)dy=0

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Q: 34. Which of the following is solvable directly by power rule of antiderivative? A. [xe"dx B. Ssin*…

A: Which of the following is solvable directly by power rule of antiderivative?

Q: Calculate . (x² + x²)e²as, where S is the cylinder with equation x² + y² = 9 for 0 < z < 10.

A:

Q: Q2] Classify the following D.E to: order, degree, homogeneous, and linear: dy 2y=x 3 dx dx

A: We can solve this as follows:

Q: Q5. If W = x² y + 2xyz , x = t², y = t + 1, z = 2t at t = 1. Find the total differential

A: Let's find.

Q: given: W = x² + 2y² + 2² x = cos (st) : y - 2s int 35² √+ chain role, find 3 × 502 8 using dw Ət

A: To solve the following problem

Q: Given : S 6x³e**+3 dx. Using integration by parts (S udv = uv - fvdu) and letting u = f(x), dv =…

A:

Q: Q.3 a) Verify Green's theorem for |(x2 + 2xy) dx + (y? + x³y) dy Where c is a square with vertices…

A:

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value. y' =…

A: We have first order differential equation and to slove this use Runge kutta 4 order method. Given…

Q: Q 4. a) Use integration by parts to evaluate Sz²cos zdz. b) Evaluate f xlog(x + 3)dx.

A:

Q: Given : S 6x³e*+3 dx. Using integration by parts (S udv = uv – f vdu) and letting u = f(x), dv =…

A:

Q: dw Find if w = xy? + x²z+yz?, x = t², y = 2t, and z = 2. %3D dt |t=1

A: Simple derivative problem....

Q: Apply the appropriate integration techniques to evaluate 9x? dx S- а. b. fxsin dr. 2 c. f(2x – 8)°dx…

A:

Q: Find the integrating factor. c. ydx + (3x – xy + 2)dy = 0 d. (x² + y² + x)dx + xydy = 0 (3x -…

A: A differential equation is in the form M(x,y)dx + N(x,y)dy = 0 and if it is not exact Then we can…

Q: Solve the following using Integrating Factor by Formulas. a.) 2y(x2 - y + x)dx + (x2 - 2y)dy…

A:

Q: Find a positive value of k for which y=sin⁡(kt) satisfies d2y/dt2+16y=0.   k=

A: Double derivative

Q: Given: J6x e* dx, Using integration by parts Suov= u= f(x), dv= 3 g(x) dx, find h(x) if |vdu = h(x)…

A: to find:- h(x).

Q: Ql: f(x.y)-y cos xy over the rectangle 0sxs , 0 sys1

A:

Q: Evaluate J.J. xy² dx dy 2 20 30 20 -30 -20 2/3 2/3

A: In the given question we have to choose the correct option from the given option . In the question…

Q: c. x²dy+ (2x³y – e*)dx = 0

A:

Q: dy + ydx %3D = 3x²y?dx,

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Q: 4. Find dy and Ay for y = 3VT-1+2x at r = 2 with dr = Ar = 0.2. %3D

A: The given equation is y=3x-1+2x. Given that x=2, dx=△x=0.2. Now,…

Q: Evaluate using integration by parts o D (x²-3) e² dx е

A:

Q: Evaluate: [S y² dV where E the solid hemisphere x² + y² + z² 0

A: We have to evaluate the triple integral ∭E y2 dV on the solid hemisphere x2+y2+z2≤9. Observe that…

Q: An integrating factor (of the form u(x, y) = x" + y") for the DE. ydx + 5xdy = 0 is O is + y * + y?…

A: Solution: The objective is to find the integrating factor of the given differential equation

Q: Find h t Trans form of decivative for d²f and d' f dt3

A:

Q: Find (a) PSD of U(t) = X(t) + Y(t) (b) Sxy (@) and SXu (@) %3D

A: Answer: For the given data, we get

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.