Suppose that x and y are related by the equation Proportionality 1 dt. Vi + 4t² |Show that d²yldx² is proportional to y and find the constant of proportionality.

Q: Solve the diff eq. (Homogenous) dy dx + x²(y² + 3) y(x³ + 1)

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Q: An insect is in a toxic environment. The level of toxicity is given by T(x,y)= 2x* – 4y° If the…

A: Tx=0⇒x=0Ty=0⇒y=0Using D-TestD=TxxTyy-[Txy2]D=0 at (0,0)   T(x,y) is minimum

Q: SOLVE USING INTEGRATING FACTOR (2y² – 3x²) d x + (2x² – x y) dy = 0; y (1) = 1 9.

A: Let's find.

Q: Convert y " (f) + (1 – t) y' (t) + e¯' y (t) = t – 5t; y (0) =- 3; y' (0) = 4 into an in tegral…

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Q: a. By differentiating x2 - y2 = 1 implicitly, show that dy/dx = x/y. b. Then show that d2y/dx2 =…

A: The given equation is

Q: ty (t+1)y + y = t²

A: Given That : ty"-(t+1)y'+y=t2 To find: solve the differential equation using determinant coefficient…

Q: x dv (2.v) - dx (V²1) dv (1+r) dx X 2 \-2 V-V²

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Q: (² + 1)³yy'(t) = 1(y² + 4)

A: Given:- (t2 +1)3y y'(t) =t(y2 +4)  To find:- General solution of given differential equation

Q: Use variation of parameters. a. (D^2 − 1)y = e^x + 1

A: Given equation is (D2-1)y=ex+1

Q: z is jointly proportional to x3 and y3. If z=490 when x=8 and y=4, find z when x=6 and y=5. (Round…

A: z is jointly proportional to x3 and y3. So,   z  ∝  x3y3 z = kx3y3

Q: (xy + x)dx = (x²y² +x² +y² + 1)dy

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Q: For y''+3y'+2y=e^-x, use the variation of parameters formula to find a particular solution. Show…

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Q: 2. Solve dx2 d²y for x = u? + 1 and y = 3u3 – 3u in terms of the parameter u. -

A: Given query is to find indicated derivative.

Q: (x + у—4) dx — (х — у+2)dy %3D 0

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Q: B. Solve the followina equation using the dete 3. 2y(x2 -y + x) dx + (x2- 2y) dy = 0

A: Given,                  2y(x2-y+x)dx+(x2-2y)dy=0

Q: 4.2(х — у)dx + (3х — у — 1)dy 3 0

A: Let's find.

Q: Determine the solution of the equation using coefficient s linear in two variables metho: (x − 3y +…

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Q: se the method of variation of parameters to determine a particular solution to the given equation.…

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Q: Solve for the general solution (4ху +3у — х) dx +x (x+2у) dy %3D 0

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Q: Evaluate. (Use C for the constant of integration.) x2 dx (1 – 25x²)3/2

A: Given,          ∫x21-25x232dx

Q: Integrate the function. y dy (25-y)3/2

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Q: find the function y(x) satisfying dx/dy=5x ^(-6/7) and y(-1)=-2

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Q: Find the general solution of the equation xy' = ky that is valid for x > 0.

A: We have to find y(x) for this equation which is valid for x>0. We use integration to solve this…

Q: (x + 2y – 1)dx + 3(x + 2y)dy = 0

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Q: 1. If y = kVx and y = 180 when x = 36, a) find k, the constant of proportionality.

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Q: Q3. Find dt 4x – 2 dx x² + 20 4t

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Q: у (4х + у) da 2 (x² – y) dy - - 2x2 + x + 2 ln y = C ans.

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Q: Show that dC 1.8x - 1.5 - dx Vx2+0.04 and hence determine the value of x that minimises the cost

A: if for a function f(x) at x=a ,f'(x)=0 then we check for f"(x) if it is positive at x=a , then f(x)…

Q: [1+ (x + y)²]dx + [1+ x(x + y)]dy = 0

A: Given: 1+x+y2dx+1+xx+ydy=0

Q: |(2 f(x)+3) dx=19 f(x)dx then equals?

A: ∫afx+bdx = a∫fxdx+∫bdx

Q: Determine the solution of 2x (y+1)dx−ydy=0

A: Determine the solution of 2x (y+1)dx−ydy=0

Q: 4. Determine dx2 - of the function y = v1– 2xt + t² |t= constant

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Q: ty" – (t+ 1)y' + y = t?

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Q: 1 Find the direct variation equation given y = 2 when x = 5

A: This question is related to direct variation. We will solve this problem by using standard form of…

Q: Suppose that y is inversely proportional to square of x. Find the constant of proportionality k if y…

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Q: Solve using variation of parameters or reduction of order (D² + 1)y = sec*x

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Q: Find the constant of proportionality k if y = 2 when X = 8. %3D k = Using the k from above write the…

A: Follow the procedure given below.

Q: using variation of parameters: - 2x + x = e t (et 1 1)2

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Q: Use the method of variation of parameters to solve. y" + 4y = 8 tan t - "/2<t<"/2

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Q: Find an implicit general solution of ( x² + dx + 1+ 4x²y², - y*) dy = 0 %3D 1+4x²y?

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Q: 5 If f(x) dx = 37 and g(x) dx = 16, find [2f(x) + 3g(x)] dx.

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Q: Solve the IVP: - 8x + 7y – 7x + 2y dy where y(2) = 9 dx Solve your solution equation explicitly for…

A: NOTE: Refresh your page if you can't see any equations. . compare this DE with  here we have

Q: 9. If f(x) dx = 33 and g(x) dx = 16, find [2f(x) + 3g(x)] dx.

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Q: An insect is in a toxic environment. The level of toxicity is given by I(x,y)= 2x* – 4y If the…

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Q: Solve for general solution using the variation of parameter method x²y" – 2xy' + 2y = xFe* find the…

A: Given DE is x2y''-2xy'+2y=x5ex. Use the variation of parameters method to solve the DE.

Q: Solve for particular solution. (x+x⁴+2x²y²+y⁴)dx + ydy = 0 ; when x = 1 y = 1

A: Let's find.

Q: If f(x) dx = 10 and F(x) dx = –7, find ſ* f(x) dxr. %3D relugte:

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Q: Is y directly proportional to x? y = 14x-8x If so, give the constant of proportionality. If not,…

A: We have the given term as y=14x-8x On solving further, we get the result as y=14x-8xy=14-8xy=6x…