Find the value of the constant A so that y = A sin 7t satisfies the equation + 2y = 4 sin 7t. dt2 Enter the exact answer.

Q: 2. Solve using any technique y" – 2y – 3y = sin r

A: First we find CF and then PI(by using the formula of PI of sin(ax)) and further find general…

Q: y" + 3y' + 2y = e¯ 2« – 10 sin(æ) - 10 -2x -

A:

Q: Solve for the general solution of (cos x cos y – cot x)dx – (sin x sin y)dy = 0.

A:

Q: (3t+t²)sin (2t)dt

A: We have to integrate the function        (3t + t2)sin(2t)

Q: dy Find the General and Particular solution of = 8 sin 4x ; y = 6 when x = 0 dx

A: Given that : The differentiable equation dydx = 8 sin 4x . y = 6 when x = 0.

Q: Find the solution of the equation cos y dy? which tends to zero as x → 0o and has the value cos y…

A:

Q: Solve the equation (x+2) Siny dx + X cosydy=1 собуду=0

A:

Q: Find the general solution of the equation y" +9y = 4 sin(3t) by using (a) undetermined coefficients…

A: To find the general solution of the equation y''+9y=4 sin3t by using (a) undetermined coefficients…

Q: Solve using the Method of Coefficients: y'' + 3y' + 2y = 7 cos x - sin x

A: The given differential equation

Q: Find the general solution of the equation using method of undetermined coefficients. ODE: y" + 9y =…

A:

Q: Find a particular solution to y" + 36y = 24 sin(6t). %3D

A:

Q: y" + 2y' = 2 – 5 cos(x), y(0) = 0, y' (0) = 1. %3D

A:

Q: Q6// find the general solution (sin-ix+- 1 dx + sin-1xdy 0

A: Note the following result of integration. We will use it in the solution :

Q: Use undetermined coefficients to find the particular solution to y'' + 5y' + 4y = - 400 sin(2t) Y(t)…

A:

Q: ∫(3t+t²)sin⁡(2t)dt

A: Given that, the integral is ∫3t+t2sit2tdt.…

Q: Solve the stated IVP using the method of undetermined coefficients.   y’’ + 3y’ = 3 sin 2t, y(0) =…

A:

Q: b) Solve to find if y = Tant VE and t = 4x-2 – secx dz b) if z = sin20, and 0 = [cos(w) + 1]² + cos…

A:

Q: cos²x sinx dy + (y cos³x - 1)dx = 0

A:

Q: Solve the equation siny(X+siny)Dy+2x²cosydy=0

A: Consider the provided question, sinyx+sinydx+2x2cosydy=0sinyx+siny+2x2cosydydx=0…

Q: What is the solution of the D.E y"- 3y' = e* sinx when solved using the | method of undetermined…

A: We need to find the solution of the given differential equation using the method of undetermined…

Q: Find an integrating factor and solve the equation (sin x+ e° ) dx + cos xcdy =0.

A: According to question sinx+eydx+cosxdy=0

Q: Q7// find the general solution 1 (sin-ix + =y)dx + sec-1xdy = 0 xVx² – 1

A:

Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. tan2y dy = sin3x dx

A:

Q: Solve the DE by eliminating the arbitrary constant of x sin y + (x^2)y = C

A: Given that the expression xsiny+x2y=C. Differentiate with respect to x.…

Q: Find a particular solution to y" +4y = - 12 sin(2t).

A:

Q: following + (Co Sx) y Solve the Sin X dy tanx %3D

A:

Q: solve for y'. y=sin-1[(ax+b)/(bx+a)]

A: Sin-1x can be written as asin(X)   So we have expression as y=sin-1(ax+b)(bx+a) We have to solve for…

Q: Use undetermined coefficients to find the particular solution to y"+ 5y' + 4y = - 500 sin(3t) Y(t) =

A: We have to find the particular solution of  y''+5y'+4y=-500sin(3t) by using the method of…

Q: Solve for the General Solution ds 5s = dt te 5t sin t %3D

A:

Q: Show that the following equation is exact and find its general solution. (3x²y+ 4y + dx + (x + 4x +…

A:

Q: dz Find x? sin(2y – 5z) =1+y cos(6zx) -

A: This is partial derivative so differentiate it as normal differentiation of z with respect to y…

Q: y = sin(Ax + B)

A: We will find the Differential equation as following.

Q: Solve the given higher order DE y" – y" + 3Dy – 5y = e*Sin 2x

A: Auxiliary equation corresponding to given differential equation: m3-m2+3m-5=0 Roots of polynomial…

Q: Evaluate by any applicable method. T/2 S cos sin y dy 60 120 60 None of the choices. Please refer to…

A: Topic = Integration

Q: | sin t cos* t dt 9.

A: We have to evaluate given integral Concept:

Q: d'y Using method of variation of parameters solve + 4y = 4 tan 2x dx?

A: d2ydx2+4y=4tan2x

Q: Solve the DE when all conditions set to zero. (D² + 4)y = sin²2x

A:

Q: (2xy* + siny)dx + (4x?y³ + xcosy)dy = 0

A: The objective is to show that the  differential equation is exact and solve it.

Q: . Obtain in two ways the general solution of (r+ sine – cose ) dr+r(sine + cose ) de = 0

A:

Q: Use the method of undetermined coefficients to solve the following equations. dx (a) dt sin(t) + 2…

A:

Q: dx +x cos(t)-sin(2x) = 0, dt sin(2.x)

A: We have to slove this ODE:

Q: Find the solution where y= 1 and dy/dx = 0 when x =0 and describe the behaviour of the solution for…

A:

Q: of Solve the initial value problem xdy + dy= ydx, yca) =6 %3D df dx find the function fox) Given =…

A:

Q: Solve the equation (x+3x³ siny) dx + (x4 cosy) dy = 0

A: Here we have given a differential equation :(x+3x2siny)dx+(x4cosy)dy=0      ......eq(1)

Q: Using a similar method to above, that is, integrating by parts twice, the following result may be…

A: In this question we have to prove Integration by using Integration by parts.

Q: 6y' = y*sinx У (0) — 1

A:

Q: Use the method of variation of parameters to determine a particular solution to the given equation.…

A: Solution is given below

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.