[The following initial value problem is defined with an exact differential equation. If the solution of this problem satisfies y(1) = B, evaluate 48² – 9B + a]. S (8zy² + az²y)dæ + (8y – 9x)x²dy = 0, ly(-1) = 1.

Q: For what value of k is the following differential equation exact? (3r² – kr²y + 2) + (đ² – 4x² +3) -

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Q: Show that the following differential equation is perfect or not, then find its general solution:…

A: Introduction: Any equation with one or more terms is a differential equation. It includes taking the…

Q: dy dx -3х а) +3y= 2xe3* b) t- +3x = 2t°, x(2) =1 dx dt

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Q: Solve the differential equation by separation of variables: yl= 6xy², y(0) = 1/ 3 Oy y = Y y Y 1…

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Q: Solve the following differential equations: 1. x(x + y)dy + (y+ 2x)dx = dx

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Q: 2 xy dy – (r' + 2y³) dx = 0 xsin 2 dy y sin- -x | dx

A: Homogenous differential equation: Let us consider differential equation of the form…

Q: (8) (4ry + 3y)dr+ (5x²y+4r)dy = 0 µ(r²y³)

A: The solution is given as

Q: Which of the following differential equations is NOT exact? Select one or more: a. (x² + 2xy)dx + x²…

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Q: 1. Find the value of a and 3 so that the given differential equation is exact: (2y³ + axy¹ - 5x) dx…

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Q: Solve the following differential equations (a) y/ = (b) = %3D ytev

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Q: Solve the separable differential equation dy dx 11x - 4√ x² +1 Subject to the initial condition:…

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Q: Use the method for solving equations of the form dy dx =√√11x+y-11 dy = G(ax + by) to solve the…

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Q: a.) 4xy" + 3x³y'-7x = sin(2x)e²x b.) 5xy+3 dy dx = 2e¹¹

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Q: Show that the differential equation dy -2 - yezy dr rezy – 2y is exact and find its solution. 3.

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Q: 5. Use the method of undetermined coefficients to solve the differential equation dy + a²y= cos bx,…

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Q: 3. Find the differential equation having the solution as of the following: a. y = ce-* + c2e¬2x + x…

A: The number of arbitrary constants in a given relation is the order of the differential equation of…

Q: :) x(x² + 1 )y' + 2y = ( x² + 1 )

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Q: The solution of the following second order differential equation xy"(x) + 2y (x) + xy(x) = 0, is:

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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.