Use the Laplace transform to solve the given initial-boundary-value problems. ди ди + =x, ат дх u(0,t) = 0, u(x,0) = 0, x>0,1 > 0, t> 0, x>0

Q: Show that the directiona f(x, y, z) = z²x + y ² at ( X (1/15" + ) ; 255. them

A: fx,y,z=z2x+y3 P1,1,2v→=15i+25j We know directional derivative Dv→fP=∇fP.v→v→

Q: use the laplace transform to solve the initial value problem y''- 4y'- 4y = t^3          y(0) = 1,…

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Q: Find the general solution of the DE s

A: Given: - The differential equation is, dydx=2yx+x3y+xtanyx2 To find: - The general solution of the…

Q: [(x²-y²)²] x+y -2 LEK 1J0 du dt

A: We have to find value of given double Integral.

Q: Use Laplace transforms to solve the IVP y''-y=0, y(0)=2, y'(0)=3. Show the complete solution.

A: Given initial value problem is, y''-y=0, y(0)=2, y'(0)=3

Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

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Q: 3) A hot cup of tea has temperature T(1) = 198 °F, one minute after it has been sitting on the…

A: To calculate the local linearization of the temperature at t = 1.

Q: Use the laplace transform to solve 3x'-y=2r;x'+y'-y=0; x(0)=y(0)=0

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Q: Plot the slope field of y=x+y using slopes m = -3, -2,-1,0, 1, 2. Sketch integral curves for…

A: First we plot the slope field and then plot the curve .

Q: Integrate the function. S dt o. O. V6-R+ sin'1 6t + C 6t o. + C 612 o. 6t 16-12

A: We can find the integral as below.

Q: Solve equation using Laplace transform ÿ +9y = 6 (t -) sin(t), y(0) = 0, y(0) = 0 %3D

A: Given the given equation is y"+9y=δt-π6sint,     y0=0,  y'0=0 Use the property of delta function.…

Q: determine the singular points of the given function, type of these points and calculate their…

A: The given function is                                      f(z)=1z2-4z+13

Q: find the linearization at x = a. y = (1 + x)^−1/2, a = 0

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Q: L(x) = b) Use the linearization to approximate 125.1 ~

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Q: Use the laplace transform to solve 3r'-y=21;x'+y'-y=0; x(0)=y(0)=0

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Q: if r'y-- 2y + 1.

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Q: Use the Laplace transform to solve the given initial-value problem. y" - 3y' = 4e2t - 2et, y(0) = 1,…

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

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Q: 10. Integral 2-t dt

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Q: Transform the function y=(1)/(2)x right 6 and vertical shrink of (1)/(4)

A: The given function is y=12x. To transform the function rightwards by 6 units and to shrink…

Q: to solve the IVP with an Use the method of Laplace transforms, impulse right-hand side and simplify…

A: Step 1: Step 2: Step 3: Step 4:

Q: linearise R = AT + BT

A: To linearise the below equation. R=AT+BT2

Q: S cos*rdr = sinxcos²x + sinx +c %3D Select one: O True False

A: (1).  The given integral is: I=∫cos4x dx