The D.E. xy = y(lnx - Iny) is Select one: a. Linear b. Exact c. Homogeneous d. Separable

Q: Which among the following DE is/are homogeneous? * 2 punt i (X +2y)dk +(ax+y) dy =0 i dxyy = ytHl x…

A: We will find out the required solution .

Q: Which of the following is a homogeneous DE? a. zydx + (x - y?)dy -0 b. y'+2ry =1 c y'+y= sinx d. xy'…

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Q: Compute the given antiderivative. Use exact values. s dz = 5 2 X +C %3D

A: The given integration is: ∫5x dx To compute the given antiderivative.

Q: The differ en tial equation yʻz + 2y'e* = 0 is (a) linear (b) separable (c) homogeneous (d) exact

A: The given differential equation is: y4x+2y'ex=0

Q: 1. Compute  E yz dV , where E is the region above z  0, below z  y, and inside x 2 y 2  4

A: Obtain the limit of integration as follows.

Q: wnich of the followi ng functrons is homogeneous? 5x - 12メy ty? Po.) sm xy Ci) eln xy 2

A: To find which of the following function is a homogeneous function. A)fx, y=5x3-12xy+y3B)fx,…

Q: Let Ly)= x²y"- x(x+2)4'+ (X+2)y as Consider the homogeneous diffeuntial equation, Lly)=0 (*) is show…

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Q: By using the multivariable chain rule, compute each of the following deriva- tives. (a) dz/dt and…

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Q: 3. y = 1+Vx eğrisi, y = 3 – x doğrusu ve eksenler arasında kalan bölgenin koordinat düzleminin 1.…

A: Given the curve y=1+x, and the line y=3-x. Find the area between the curve, line  and bounded by the…

Q: Evaluate S S f3zdV where E is the solid enclosed by z = 1 and z = x2 +y?

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Q: The bending moment, M, varies with distance, x, from one end of a beam according to: 1 wx2 + C1x +…

A: From the given equation. M=-12wx2+c1x+c2    ....1

Q: tind the value of the consrant (min) that makes the D-E j X dx -CyfmX) dy so (Homogeneous, exact,…

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

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Q: Given: Sox?er*+3, dx. Using integration by parts Sucv = uv - Svau), and letting u= f(x), dv= 3 g(x)…

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Q: Evaluate (l. yz dV where E lies above the plane z = 0 and below the plane z = y, and inside the…

A: Given, ∫∫∫EyzdV, Where E lies above the plane z=0 and below the plane z=y and inside the cylinder…

Q: 2. Consider the DE y(4) – 4t²y" + 4y" = 0. (a) Is the DE linear? (b) Is the DE homogeneous? Why? (c)…

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Q: Under a change of variables z = u°/3, y = v²/2 , the infinitesimal element of area dædy becomes 6uv…

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

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

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Q: 3. Given f(x,y) = xy + y2 +1° ey Verify that fry = fyx %3D

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Q: se Usa Grean's Thaoram to ecaloate the boundary of the region (travarsad cantarclodase) acadrant…

A: Given data-                   ∫c( ex + y2)dx +( ey + x2)dy. Where, e = Boundary of the region. We…

Q: find the indicated extrema, assuming that x, y, and z ar = xyz z - 12 = 0

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Q: Evaluate dV, where E is the solid in the first octant bounded by r2 +y? + z2 = 1 E and a2 + y? + z2…

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Q: The function f (x,y) =e/*+3tan( y/x) is homogeneous of degree A) 3 B) 2 C) 1 D

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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: Suppose that w = xe"/, where x = t², y = 1 – 6t, and z =1+ 4t. dw Find dt

A: w=xeyz, where x=t2 , y=1-6t and z=1+4t

Q: By making an appropriate change of variables, evaluate the double integral = || (x + y)e²-y° dædy R…

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

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Q: Find Homogeneous DE y'-ay=0

A: Given that: y'-ay=0

Q: Calculate the following antiderivatives: 12t 2t° – 2 dt = +C. (b) u9/4 + 5yū du = +C. dz = +C.

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Q: Evaluate S S12zdV E where E is the solid enclosed by z = 1 and z = x² + y² 2. Immmmm

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Q: Solve the DE, dy =y²-a? E, = , using the homogeneous method. ry (a) Hint: Rewrite the RHS as 2 -…

A: dydx=y2-x2xy⇒dydx=y2xy-x2xy⇒dydx=yx-xy⇒dydx=yx-yx-1 Now put, y=vx⇒dydx=v+x·dvdx

Q: The linear DE.s is called homogeneous if * R(x) is equal zero True O False O

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Q: Find the Particular antiderivative that satisfies the following conditions:   dM/dt= ((5t^2)-8)/t^2;…

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Q: 10- Evaluate JJI where E is the region that lies inside the cylinder Vx2 + y?dV E x? + y? = = 16 and…

A: Here we use polar coordinate and Jacobian .

Q: Given that the total flux across the surface, S of the tetrahedron bounded by the planes x= 0, y=0,…

A: Given Vector field is F = 2xi + 3yj - zk

Q: 1 Evaluate dV, where E lines between the spheres a2 +3? + 22 = 1 and E 22 + y2 + z2 = 9 in the first…

A: Solution

Q: Let y = 5x + 4c +3. If Ar 0.1 at z 5, use linear approximation to estimate Ay

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Q: Evaluate 7x dV where E is the region that lies inside the cylinder x2 + y² = 8 E and between the…

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Q: The linear DE.s is called homogeneous if R(x) is equal zero True O False O

A: True

Q: dz Find given: dt z = xe", x = tº, y = 1+ 4t

A: Given,          z=xe3y , x=t6 , y=1+4t

Q: Sove the following EDO (Homogeneous) c) (x³ + y³)dx + xy²dy = 0

A: First we rewrite the given differential equation in the form of Bernoulli equation, after that we…

Q: dx 4V3 – 7t x(9) = 8. %3D %3D %3D dt

A: Finding x from the given conditions.

Q: dy The D.E. y? – a? can be classified as %3D da x²y (A) First-order linear (B) Separable (C)…

A: The given differential equation is                                                  dydx=y2-x2x2y…

Q: given z= f(x,y), where x = g(s,t) and y = h(s,t). chain rule for dz/dt is

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Q: The function f(x,y) is homogeneous of degree one. cos a) True b) False.

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Q: Evaluate III Vx2 + y² dV E where E is the region that lies inside the cylinder x2 + y2 = 4 and…

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Q: dy The D.E. y2 – a? - can be classified as %3D dæ (A) First-order linear (B) Separable (C)…

A: We break this into simplier form then identify it's property.