a) Find the value of 2, for which the following differential equation will be an exact DE:

Q: syidr + [2yłn () + 3siny]dy: 6. x²+3x 3y?dx 5x ;when x = 1, y = 0 x+3,

A: Given, Differential Equation:  3y2x2+3xdx+2y ln5xx+3+3 sin ydy=0when, x=1 and y=0 To find: The…

Q: y' + p(x)y = q(x), p(x), q(x) E C(I)

A: We have to find the general solution of differenrial equation

Q: a) (e" +1) e*dx + (e* +1)"e*dy = 0 1 1 dy +y dx dy y? -1 c) dx x -1 si y (2) = 2

A:

Q: y = Ce2*cos3x + C2e2xsin3x

A:

Q: 1. (2xy² + ye*)dx + (2x²y + ke* – 1)dy = 0 2. (6xy³ + cos y) dx + (kx²y² – x sin y) dy = 0 %3D

A:

Q: (y - x + 3)dx + (x + y+ 3)dy = 0; x = 1; y = 4

A: This is the question from differential equations.

Q: Solve the following Differential Equation using variable separable. dr = b(cos ϕdr  +  rsin ϕdϕ)…

A: dr=bcosϕdr+rsinϕdϕdr=bcosϕdr+brsinϕdϕdr1-bcosϕ=brsinϕdϕdrr=bsinϕ1-cosϕdϕ                           1

Q: Solve y' = + 8 ln x + 10 with y(1) = −2 Provide an exact answer (i.e. no decimal approximations)

A: To provide an exact answer to the following differential equation.y'=yx+8 ln x+10 with y1=-2

Q: zy – yln ) = = 0, 2y² + z²

A:

Q: 3 (d²x)². 7 2 y (dx)² + y ² (dx) ² + 3y || 5x

A: Order of a differential equation  The order of the differential equation is highest order of the…

Q: Determine whether the following equation is a solution to the corresponding differential equation.…

A:

Q: 6) ( 2y - x ) dx + 3xy?dy = 0 %3D

A:

Q: y" +4y' + 3y = 8(t)

A:

Q: 38. Sports You throw a softball into the air with an initial upward velocity of 38 ft/s and an…

A:

Q: (t²e' – 4x²)dt + 8txdx = 0

A:

Q: Solve the following differential equation: yde+xdy 1-x²y² +ædr=0. = constant.

A: Given that the differential equation ydx+xdy1-x2y2+x dx=0

Q: 1 y' = 4x Yp = 2 4x 2x

A:

Q: y" + 4y = 3 csc²(2t)

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.