Determine the type of the following equation and reduce it into it's canonical form: - y zyy = ry, (r +0, y +0).

Q: Show that cos(wt – B), cos wt , sin wt are linearly dependent functions of t.

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Q: Find the orthogonal trajectory of y = c1(sec x + tan x)

A: Orthogonal trajectory: - Orthogonal trajectories can be defined as lines or curves that meet the…

Q: Find a direction in the xy-plane in which f(x, y) = e¹-xy has zero change at the point P(1.0. e).

A: We know directional derivative formula Du→fa, b, c=∇fa, b, c.u^ Lets say u→=cosθ, sinθ be the…

Q: Match the following equation with the direction field. y'(t) = - !

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Q: Show that z=tan-1(2xy/x^2-y^2) satisfies the Laplace equation

A: The given equation is, z=tan-1(2xyx2-y2). Obtain the partial derivative of z with respect to x as…

Q: Find the direction field for the given DE. By hand, sketch an appropriate solution curve passing…

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Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z = x² + 3y² , x…

A: Tangent line equation problem....

Q: Evaluate eVf •dr where f(r,y, 2) = 4rye² and C is the path parameterized by r(t) = cos² t i +…

A: Given: fx,y,z=4xyezrt=cos2ti+sin2tj+tantk0≤t≤π4 Formulas used: ddxxn=nxn-1ddxex=exddxfgx=f'gx·g'x…

Q: Demonstrate that the functions Y1 = a", y2 = sin(x), Y3 = xe* are linearly independent on R. 9.

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Q: Reproduce the given computer-generated direction field. Then sketch an approximate solution curve…

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Q: Find the solution u(t, x) to the system Jau +30₂u+u²=0 for t≥0, 20, u(t = 0, x) = cos(x). Start by…

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Q: Use the given computer-generated direction field to sketch, by hand, an approximate solution curve…

A: To plot the solution curve on the given slope filed for the solution y(0) = -4.

Q: 3. Find the orthogonal trajectory of y = c sin x.

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Q: The position of a particle is defined by the vector r(t)=⟨sint,cos2t⟩. Find the maximum speed of the…

A: r(t) = ⟨sint,cos2t⟩ Hence, v(t) = ⟨cost,-2sin2t⟩

Q: find the decomposition of a(t) into tangential and normal components at the point indicated, as in…

A: Given: r(t)=(t,cost,sint)t=π2

Q: Evaluate fs xyz dS where S is the triangle with vertices (1,0,0), (0, 2, 0), (0, 1, 1).

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Q: Find the point on the graph of z = 3x2 – 2y? at which vector n = (-12, –16, –2) is normal to the…

A: Shown below

Q: Express the given parametrization in the form y = f(x) by eliminating the parameter. x = 5t + 2, y =…

A: Given

Q: Use the canonical Euler equations to find the extremals of the functional SV + ya Vi+ ya dx,

A: Consider the equation

Q: Reproduce the given computer-generated direction field. Then sketch an approximate solution curve…

A: Find your answer below

Q: Use laplace tansform y"+ + 4y" +qy'+1Oy= - 24+e y1o) =0, yl0) = -4 , y"O) -1o %3D

A: We use Laplace Transform to find function in t

Q: ) Eliminate the parameter t to find a Cartesian equation for: x = t² and y = 3 + 5t. and express…

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Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: Obtain the general solution of the Laplace equation in Cartesian coordinates.

A: Consider the Laplace equation for Cartesian coordinates ∂2u∂x2+∂2u∂y2+∂2u∂z2=0, where u=ux,y,z.…

Q: Show that the Euler-Cauchy Equation ry" + ary + by = 0, r+0 can be transformed into the constant…

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Q: Show that the function f(x; y; z) = 2z3- 3(x2+y2)z  satisfies the Laplace equation.

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Q: The vector parametric form of the tangent line to r(t) = (3t², ¿, t – 1) at t = -5 is

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Q: Find an equation for the tangent plane to the graph of z = xe' cos z – 2 - at the point (2,0,0). 1.…

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Q: 9. Demonstrate that the functions Y1 = x2, y2 = sin(x), y3 = xe are linearly independent on R.

A: Recall: If y1,y2 and y3 are the given function and         Wy1,y2,y3x = y1y2y3y1'y2'y3'y1''y2''y3''…

Q: 3z +1 (z+1)(2z – 1)

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Q: Find the Direcctional derivatve of the function foxxy,z)=tan(xjz) aut point (t,2,4) in the direction…

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Q: Find the streamlines of the flow associated with the given complex function. f(z) ==—=/ (x(t), y(t))…

A: To Find: Equation of Streamlines for the function f(z)=1z¯.

Q: Solve X' Uxx - Y Uyy = 0 x,y>0 also find its canonical form

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Q: Find the vector equation of the tangent line to 7(t) = 2 (e1 %3D

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Q: Find the Jacobian J of the transformation x = r cos(0), y = r sin(0).

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Q: Given F = xyi + 1(x – y) j+ 1(x + y) k, (1) Compute the fundamental cross product F, xF, =

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: Let h(r,y) = r'e. Find its linearization at the point (1,0) and use this to approximate f(2,0). %3D

A: Given function is h(x,y)=x2ey we have to find linearization at point (1,0). then to approximate…

Q: An airplane is flying in the direction 25° west of north at 800 km> h. Find the component form of…

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Q: An airplane is flying in the direction 25° west of north at 800 km/h. Find the component form of the…

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Q: Use the Chain Rule to find zz and zy given sin(u) tan(v), u = 3x + y, and v = x – y. %3D

A: Given z = sin(u) tan(v)where u = 3x + yv = x - y

Q: Find the image of the line z =3 +iy under f(z) = e

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Q: Express dw/dr and dw/as as functions of r and s using chain rule w = In(x + y + z*), x = re sin r, y…

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Q: Evaluate I=∫C(sinx+4y)dx+(5x+y)dy for the nonclosed path ABCD. A=(0,0), B=(1,1) ,C=(1,2), D=(0,3)

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Q: Find the orthogonal Trajectory of y=c sinx.

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Q: draw the slope field for y' = x² – y², then use it to sketch three solution curves. %|

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.