The Profit from the Sales of x units of radi ators for radiators for generators is Biven by PX Y)= -x>-y☆ 8X +4Y. Find values of x ĕ y thet tead to a mayimum Prefitif the firm Must produce a total of b (six) units of radiators auto mobites ď Y units of

Q: Solve using crama's rule: 2x - 2y + 3z = 13 5x - y + 4z = 11 x + 3y - z = -10

A: We solve the system using Cramer rules

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Q: 8. Find the partic ular solution of x²y" + xy' = 1; y = 0 and y' = 1/2, when x = 1.

A: We have to find the particular solution of x2y''+xy'=1 ; y=0 and y'=12 when x=1.

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Q: state where in the ty-plane the hypotheses of Theorem are satisfied 7. y′=(t2+y2)3/2

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Q: 3. If V = (3r'y-1,x2'+y',-2r:"). Find grad divl at the points (2,-1,0).

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A: The solution of differential equation y’’+6y=0 is

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A: Double differentiate to prove the given

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Q: (D³ + 2D² − 5D − 8)y = 0, when x = 0, y = 0, y' = 0, y = 2 - -

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Q: az Find at (2, -2, 1) if x2 + y? + z2 = 6xz+ 6yz + 21 %3D 8. %3D %3D dy %3D 25 25 1.

A: Given,x2 + y2 + z2 = 6xz + 6yz + 21

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Q: f(x) = 2x5 + 15x4 - 3x3-4x2+ 7x+ 14 1)Trapeaoidal rule 2) Trape20idal rule with n=2 3) 1/3 Simpson…

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Q: Verify that y = ODE y" + 3y' + 2y = 4x². -4e-x-2e-2x + 2x² - 6x +7 is a solution of the SHOW ALL…

A: We have to verify that y=-4e-x-2e-2x+2x2-6x+7 is a solution of the ordinary differential equation…

Q: Find general Solution of y + +y+ 4y = Ct1)e Using method of vanafion.

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.