Find the solution of the given initial value problem in explicit form. () T sin(2x) dx + cos(9y) dy = 0, 9 y(x) =

Q: Solve Differential Es: 1. 5y" + 6y' + y =0 2.9y" - 12y' + 4y =0 3. y" + 4y =0 Sin qx) ax Use: y = C₁…

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: x-1/2c (4) y = x sinh 2x – cosh 2x

A:

Q: Use the Method of Undetermined Coefficients to solve y′−(y/2)= cos(2x), y(0) = 1. Put your solution…

A: y'-y2= cos(2x) -(i)The homogeneous DE isy'-y2=0.·. D-12y=0Where D=ddxThe auxiliary equation…

Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

A:

Q: B) Find the general solution of the equation by using (Undetermined Coefficients method) d'y dy de =…

A: Solution of the differential equation using undetermined method

Q: (e – y cos (x)) dx + (2xes (ey – y (xy) + 2y) dy x Cos cos = 0 3.

A: Exact differential equations

Q: (D²1)y = 5 sin² x ; y(0) = 2; y'(0) = -4

A:

Q: Find the general solutions (implicit or explicit) to the following equations. (a) y' = e3x-2y + x²…

A: First order ordinary differential equation.

Q: b. Solve the initial value problem: f (x)= sin x +e2, f(0) = 4 1 f (0) 2

A: Given: f''(x) = sin x + e2x, f(0) = 14 and f'(0) =12

Q: c) Solve the initial value problem (1 + cos² t). 21) dx dt - x sin 2t = 4t² + 5t +4, x(0) = 2

A:

Q: Solve (x + sin(y))dx + x cos(y)dy = 0 and find the solution passing through (2,7)

A: Given: We have to solve the given differential equation and find the solution passing through

Q: Solve the initial value problem (3x² + y cos x)dx + (sin x - 4y³)dy = 0, y(0) = 2 Write the solution…

A:

Q: y(4) co +2y"+5y" = t +e s(2t) +t cos (3t)+te' s(3t)+te'

A:

Q: Find the solution of y" + 3y = 126 sin(3t) + 54 cos(3t) with y(0) = 2 and y' (0) = 7.

A:

Q: 3. Show that the equation (6ry – y*)dx + (4y + 3x² – 3xy²)dy = 0 is exact. Hence solve the equation…

A: Solution:

Q: QI/ Aaswer the following: a) Solve the following initial-value problem: xe dx + (y - 1)dy 0; y(0) =…

A:

Q: 5. Solve the particular solution of (D2 + 1) y = sec (x) tan (x) using variation of parameters

A:

Q: 4. Consider the initial value problem dr (12t sin (4t))i + (4t√² +1}} +(0) -3i-j (a) Solve the…

A: Consider the initial value problem. dr→dt=12t sin4ti→+4tt2+1j→r→0=3i→-j→ (a) To solve the…

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y"-81y'…

A: Sol:- y'''-81y'=te-9t+10cos9tFirst , find the yh:-yh is the solution to the homogeneous ODE…

Q: Find all general solutions of y'(t)=(t+1)(y(t)2-1). Leave the solution as the form y(t)= an…

A: Given data:     The given differential equation is: y’(t)=(t+1)(y(t)2-1).     The given differential…

Q: c) i) Find 2 sin cos (1 + sin 8)³ 1) Solve the differential equation sin 2x cos² y (1 + sin x)³ IL…

A:

Q: Solve the Euler equation d²y dy 3x? dx -5у%3D0 +x dx given that y(1) =1 and y'(1) = 2.

A:

Q: sin (3x) dx + 2y cos³ (3x)dy = 0

A:

Q: Solve the following equation for y(x): y" + 4y = 6 cos 3x + 20 sin 3x

A:

Q: Find the 3rd derivative of (1 + 2y)³ + eª (sin² y) - 3y cos(e=? )

A: Given data (1+2y)3+ex(sin2y-ycosex2=3y and find 3rd derivative or d3dx3=?

Q: cosy dx+[x+le dx +[x+1

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.