S Sz(x² + y³)dxdy, wherein B = {(x, y) E R²; 0 < x² + y² <4}.

Q: 9-x² - y² SS. 0 9-x² 0 √√x² + y² dz dy dx 2

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Q: Q1\ solve the equation : d²y dy + 7 +12y= 1 for initial condition y(0)= 1 y(0)=2 dx2 dx

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Q: 1 Q2: Evaluate fo y² (x² + y²) dx dy

A: Given :∫01∫01-y2y2x2+y2dxdy

Q: dy ху+3x-у-3 7. Ans: y-x+In y+3, %3D = C dx ху-2х+4у-8

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Q: Q2. Show that dx ax + by di dy = cx + dy di can be written as + yx = 0

A: The given system of differential equation is. dxdt=ax+by                     ......1dydt=cx+dy…

Q: ven f(x,y) = -2xy² where x = 5t and y = 8t2. Findf' (t) at t = 3. %3D

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Q: a. (2ry*e + 2xy + y) dx + (r²y*e -x²y² – 3x) dy = 0; when x = -1, y = 1

A: As per our guidelines we are supposed to answer 1st question only. Please repost rest questions...…

Q: Evaluate " " So s L dz dx dy rvZ c3y (8-x²-y² Jx²+3y²

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Q: Obtain the particular solution when x = 1 and y = 1 3 y°) dx 3 - x(x + y) dy = 0

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Q: dy is xy dx dx The general solution of y2 + x2 dy Other O

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Q: 8. Jydx + (1+ x)dy = 0,,when x = 1, y = 4

A: Differentiable equation can be solved separating the variables on each side and then integrating…

Q: dy is dy xy dx dx The general solution of y² + x² "

A: Solution is given below:

Q: Find the solution of (x² – xy – y²) dx + xydy = 0 -- -

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Q: dy 2x2+2x+1 Q 3. Examine dx for y(0.6) by RK-4 method if y(0) = 1, h = 0.2. x2+5x

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Q: -2 (x² - y²)²] Evaluate: S₁ S² P₁² dx dy x+y

A: Let's evaluate given double integral.

Q: d²y 2) Obtain a particular solution for d*y dx+ + + y = x³ + 2x +1 dx2

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Q: 6. General solution is y = x² In x + Ca² , EXERCISE 6. dy 2y = x? dx

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Q: 4. S Sp(x² + y³)dxdy, wherein B = {(x, y) E R²; 0< x² + y² < 1}

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Q: Sin²y dy V1 -x, given that y(-3) = 0. dx 2) Snow that the general solution for (x2 +x-6)dy = 4y dx…

A: Given that  The following differential equations

Q: 4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

A: Consider the given expression, ∬Rfx,ydA=∫04∫2-y24-yx2-x33dxdy This suggests that the region spans…

Q: Q4 Find for all of : dx 1- y = xvInx 2- y = 3 x(x-2) %3D x²+1

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Q: dy=y°-1 ex 2y

A: This is Separable differential equations

Q: Q3: van fy = xy-1+ x.ln(x) J f(x,y) = x' + y* if it was

A: To find the partial derivative

Q: What is the solution of the DE e dx – x² dy = 0? A. y = (c - B. y= In (c - C. y = In (c - x) D. y =…

A: As per our guidelines we are supposed to answer one question, kindly repost the remaining question…

Q: Q4) Use the chain rule to express dy /dx in terms of x and y t2 y = t2+1 and t = 3x3 – 3 where x =1

A: Given y=t2t2+1 and t=3x3-3 and x=1

Q: Find the particular solution: (y4 – 2xy) dx + 3.x² dy = 0; when x = 2, y = 1 %3D

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Q: y² + 5 dy J y²Cy² + 25)

A: Given problem:-

Q: (x³ + y² + z) dx dy dz. 2 Evaluate

A: To evaluate the integral

Q: 5. Evaluateſ, x²y dx + xy² dy where C is given by: r(t) - 3t v(t) – et 0<t< 1

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Q: Find the general solution: k^2 dx+(x-y+k)^2 dy3D0

A: Given that: k2dx+(x-y+k)2dy=0     NOTE: As per our answering guidelines, we can only answer 1…

Q: y et 2x *Sec2X Pinel dy o

A: By using these differential formulas that are ddxex=ex, ddxax=axlnx where a is constant,…

Q: (c) Find the specific solution to d²y dx² when x = 0,= 0 and y = 1 +4 dy dx + 5y = 0

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Q: dy Given y x" In (2x), determine dx ax"- In (2x) + a-1 a.a"- In (2x) + 2.x O...n 1 None of these ax…

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Q: SSS(x² + y²) dV where E lies between x² + y² +z² = 4 and x² + y² + z² = 9

A: E

Q: xy3dy − (x4 + y4)dx = 0 find the general solution of the differantial equatiton

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Q: Q11) The solution of (1 – y² )dx + (1+ x² )dy = 0 is: %3D

A: 1-y2dx+1+x2dy=0 On simplification, we get ⇒1-y2dx=-1+x2dy⇒dx1+x2=-dy1-y2

Q: 4. ydx + x(Inx - Iny - 1) dy = 0, when x = 1, y = e

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Q: Find the exterma R-{ (ny ): xy zo} 2. F(xry) = x² +y?- メッ ×り

A: To find extrema first we differentiate the given function with respect to x and y, then after…

Q: - 3-z2-y 2. Evaluate L* L z dz dy dx -5+x²+y²

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Q: [" In(y+z) e dxdzdy = [Show your solution.]

A: Given that,

Q: Find a particular solution: (x2 + 6y2) dx – 4xy dy = 0, when x = 1, y = 1

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Q: Solve the DE. (1+x²)dy + [(1-x)²-xe^-x]dx = 0; when x = 0, y = −2

A: This is a problem of ordinary differential equation. first of all we will simplify it into dy/dx…

Q: y" – 10y' + 34y = 3x2 + x – 1 || | (D² – 10D + 34)y = -cos3x

A: 1-D-1 = 1+D+D2+D3+.... Note : As per our Guidelines, we are supposed to answer first question.

Q: find 04 O B O 7 O -12 af ду dy' given f (x, y) = e + 2xy² – 4y at (0, 3) -

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Q: 2. x3 – y3 = c³, find y" %3D d²x 3. x* = at?, find dt2

A: we need to find d2ydx2 from equation x3-y3=c3

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: d*y d²y dy .3 Obtain a particular solution for dx4 + + y = x³ + 2x + 1 dx dx2

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Q: (b) If z = 9t²e 4t, find 4 dz dt

A: Given.