Identify the exact differential equation. O (1+ y?) dæ + (1 + 2y) dy = 0 %3D O sin 3x da + cos 3x dy = 0 O (y4-y sin x) de + (4xy + 3y2 cos r) dy = 0 %3D O (y² + ya) dx + a²dy = 0

Q: Determine whether the given differential equation is separable. dy + 2 sin (x + y) = 0 dx

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Q: dy The general solution of is da O 2x3 + a²y? = C O 2x3 = C 2y3 + a?y? = C O 2y3 = C (E) +

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Q: (a) Find the general solution of the differential equation (2xy +3y)dx (2ry + x²)dy = 0. (b).…

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Q: Solve the differential equation e sin 2y dx - 3x-cos 2y dy A - 3ln(sin 2y) = C B +3 In(cos 2y) = C…

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Q: Show the following differential equation is exact, then solve it. [sin(xy) + xy cos(xy) – 8x]dx +…

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Q: 1.1 (x + siny)dx + (xcosy – 2y)dy = 0

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Q: Solve x (az + √2) dx y (az + √2) sin (ay²) dy + (az − √2) dz = 0 4√/2ln |az + √2 = C 4√/2ln|az +…

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Q: Solve the differential equation y tana+y = 3 sin r. %3D sin I A sin a B sin r + C Cos a c - sin I +…

A: We have to solve the differential equation: y'tanx+y=3sinx

Q: Solve the differential equation: Cos(x)dx + ( sin(x+y) + sin(x– y))dy=0 Hint: sin (A ± B) =sin A cos…

A: Given differential equation  cos(x) dx + {sin(x+y) + sin(x-y)}dy    Using identity of sin(x+y) and…

Q: For what value of is the differential equation (6zy + cos y) dr + (3ka²y? – 3y?) dy = 0 exact?

A: Exact differential equation

Q: Which of the following is a linear differential equation? O da-t{1+t²) sec² ædt = 0 O…

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Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

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Q: Show that (2x cos y + z siny) dx + (xz cos y – x² siny) dy + x siny dz is an exact differential.…

A: Given differential equation,2x cos y z sin y dx + xz cos y -x2 siny dy + x sin y dz =0

Q: Part I. Calculation: Find the solution of each Differential Equations. 1. sin x siny dx + cos x cos…

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Q: Solve the differential equation: cos(x)dx + ( sin(x+y) + sin(x –y))dy=0 Hint: sin (A ±B) =sin A cos…

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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.