Show that the following equations are exact. Find solution. (a) dx dy_x– y³ + y² sin x 3xy² + 2y cos x (Зу?- х?) dy (b) ys dx = 0 y(1) = 1 2y4

Q: 54 (b) y =. sin 2x. 4 Find

A:

Q: 3. Verify that ysin x-xy =0 is a solution of the equation y(cosx-y)dr+(sin x- 2xy)dy =0.

A:

Q: Cos X- cosy Jax-sinxsiny dy=2

A: A differential equation of the form Mdx+Ndy=0 called exact differential equation if ∂M∂y=∂N∂x and…

Q: Solve d²y dx² - cot x dy-sin² x.y = cos x - cos³ x. 2 dx

A:

Q: 2. f cos³ (20x)dx

A: Given :

Q: (5) If y = sin(3x) the find y"

A: We have given trigonometric equation  y=sin3x y'=dydx y'=ddxsin3x y'=cos3x·ddx3x y'=3cos3x…

Q: (sinxy +xy cos xy) dx + x² cosx y d y = о

A: The solution is given as

Q: Solve d'y dx² cot x dy - sin² sin²x.y - dx = cos x - cos³ 3 OHS X.

A:

Q: If y = cos¹ (v₁²), X = find dz? 1 Vu² +1 2= ln (2x-3y)

A: Consider the given equations, y=cos-1vu2x=1vu2+1z=ln2x-3y here we need to find the value of dz.…

Q: S(;+ sin(x) – Vx²) dx

A:

Q: (e) sin(2x) sin(x) dx.

A: ∫sin2xsinxdx

Q: dx (x²+4x+13)3/2 ſcos5(x)sinª(x)dx f) S g)

A:

Q: dy Find dx

A: Given: y=tan-1(sin(3x)+cos-1(cos(x))) Find dydx

Q: dy -y'sinx is: dx The solution of Select one: a. y3cosx+ C O b. %3D COSX-C C. V=3 CO5X + C d.…

A:

Q: 8) Given the function y =x – 3x+1 dy Find the derivative, dx

A: Solve by derivative of given function

Q: S(6Vx + 3 cos x - 8)dx

A:

Q: 1. f cos³ (tan x) sec² x dx

A:

Q: I. Eliminate the arbitrary constants -3x y= C, e sin2x + - 3x Cze cos 2x

A:

Q: sin If y = show that (1- x²) 1-x -1 x. d'y -3x dy drソミ0 dx? ーy=

A:

Q: y+y=sin(x), where y(x) = 1.

A:

Q: Jx' sin x dx

A: we need to evaluate, ∫x2 sin x dx this integral can be done by integration by parts. ∫u·v dx = u·∫v…

Q: 3+6 b. (2xy-sin x) dx + (x-Cos yldy

A: Topic:- solution of differential equations

Q: g. cOS x Vsin x dx

A: Let sinx = t

Q: J₁/₂ ( x ) = 2 TX .sin x

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.