Solve the following differential equation with the boundary condition y(0) = 0, 3/(0) = 0 dy 2 (y – x) dy = 2(x – y) dr dr²

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A: We have to use Linear Approximation.

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Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

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Q: Find a linearization of the differential equation for x near 0.

A: Given data from the problem are :

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A: Differentiating with respect to x, we get

Q: Consider the following differential equation: (12xy3+32ysen(xy)cos(xy))dx+N(x, y)dy=0 Calculate N…

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Q: = t?y – y + t? – 1, y (0) = 1 dt dy Solve the differential equation

A: Given: dydt=t2y-y+t2-1   We know that; ∫1ax+bdx=1alnax+b+C And The Power rule: ∫xndx=xn+1n+1+C ;…

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Q: dy Q6. Solve x – 2y = x' sin² (x) using first order linear differential equation. dx

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A: We have  dydx=e-yx2 Lets use variable separable method

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Q: Write an equation for the function graphed below 15+ 14+ 13+ 12+ + + + -7 -6 -5 -4 -3 -2 -1 -1 -2 -3…

A: A following graph:To Find:Equation of the above graph.

Q: Solve the separable differential equation dy = 0. 8x – 6yVx? + 1 dx to the initial condition: y(0) =…

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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.