10. What is the integrating factor of the differential equation * y = csc a-ycot a tan a sec x O Option 1 Option 2 sin a cos x

Q: y" + 2y' + y = 7 + 75 sin 2x

A:

Q: 5. For what values of r does the function y = e™* satisfy the differential equation 2y" + y' – y =…

A: Given , differential equation       2y" + y' - y = 0   (2D2 + D - 1)y = 0 The auxiliary equation of…

Q: 5. Show that the differential equation y" +a²y = f(x), y(0) = y'(0) = 0, has 1 y(x) = -…

A: proof:-we have          y(x)=1a∫0xf(t)sina(x-t)dt   ⋯(i) differentiate by leibnitz's rule(i) , we…

Q: 18. What is the integrating factor of the differential equation y' =cscx-ycotx ? a. tan x C. sinx b.…

A: This is a question related to differential equation. Based on the formula of integrating factor we…

Q: What is the general solution of the differential equation y" +4y= tan 2x? Oy C1 cos 2x + C2 sin 2a -…

A:

Q: Solve the differential equation by variation of parameters. y" + y = sin?(x) sinx ( sin’'x cos (x) +…

A: Solve the above questions

Q: What is the integrating factor for the linear differential equation 2(y - 4x^2) dx + x dy = 0?.

A: Given:  2(y - 4x^2) dx + x dy = 0

Q: Find a homogeneous linear differential equation wit Gcosh 2x coc E 2x cin 5

A:

Q: find general solution of following differential equations: y'tanx=2y-8,y(1/2pie)=0

A: Given differential equationy'tan x = 2y-8⇒ y' = 2ytan x- 8tanx         ∴ y' = dydx⇒ dydx - 2tan x. y…

Q: Show that y = cos xsin x is the solution of the differential equation y'+y tan x cos x

A:

Q: Obtain the solution to the differential equation: cos*x- cos"y dx + cosxsin 2ydy = 0 a. cos*y(1+…

A:

Q: By using variation of parameters, what is a possible value for u' for the differential equation y' +…

A:

Q: d) sin(x)y' + cos(x)y = tan(x)

A: We have to solve

Q: Consider the differential equation y' = x+ y. Use Euler's method with Ax = 0.1 to estimate y when x…

A:

Q: Find the particular solution to the differential equation y' + ytanx = sin2x with the given boundary…

A: Given:         Differential equation y'+ytanx=sin2x            y(0)=1 This is in the form:…

Q: The integrating factor of the linear differential equation + (tanx)y = x is, cost log(cosz) secr O…

A: Third option i.e. " secx " is the correct answer. Thankyou !

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin x…

A: Eliminating arbitrary constants a & b using derivatives.

Q: I. dy tan(x) dx Cos (x) + x²

A: Given equation is dydx=tanxcosx+x2   What is the best way to solve the First Order Differential…

Q: a. Circle of radius 1 and centers on the line y = x

A: The solution is given as

Q: 1. Form the differential equation by eliminating the constant A and B from y = emx (A cos nx + B sin…

A:

Q: The elasticity of demand of a service is given by E(q) = 1 - (p + 1)-1 where E(q) = pq'/q [note that…

A:

Q: 5. The differential equation (3x'e' - 2xx+ (r'e' -sin y ldy = 0 is exact because ON

A: Partial differentiation is needed to be done after identifying M and N

Q: Show that cos x is the integrating factor of the linear differential equation dy/dx= sec x+y tan x

A: Integrating factors are useful for solving ordinary differential equation  that can be expressed in…

Q: dy Show that given differential equation da y cos z + sin y + y sin a + r cos y +x 0 is Exact and…

A:

Q: 4. y" +2y'+ = cos a COS

A: We will solve the problem

Q: Use separation of

A: Given,                     7dydθ=eysin2θysecθ.

Q: 1. What is the integrating factor of the differential equation ydx – xdy = 0 using case 1?

A:

Q: 9. Use separation of variables to find the general solution of the differential equation. dy = sinx…

A: option b is correct . see 2nd step.

Q: al csc x y cotx

A: We have to find the intregating factor of given differential equation.

Q: 7. Find the differential dy of the function y = x (1-cos(x)). If the error in x is ", find the error…

A:

Q: Use separation of variables to find the general solution of the differential equation. y- dx 4…

A:

Q: 15. x" + x = tan t; x=-(cost) In(sect + tant)

A: Given, x''+x=tant x=-costlnsec(t)+tan(t)x''=cos(t) ln(tan(t)+sec(t))+tan(t)

Q: 4. y" + 4y = sin² 2x when y () = 0; y' ( = %3D

A:

Q: 5. With the substitution cosy == differential equations sin y dy – cosy(1 – x cosy)dx=0 reduced to a…

A: Substitute  cosy=1tNow differentiate it with respect to t,-sinydy=-1t2dtsinydy=1t2dt

Q: What is the integrating factor of the differential equation (5xy + 4y² + 1) dx + (x² + 2xy) dy = 0?…

A:

Q: By using variation of parameters, what is a possible value for u'1 for the differential equation y''…

A:

Q: x*y' = -x³y – csc (xy)

A: Given- x4y'=-x3y-cscxy To Find- The general solution of the above differential equation.

Q: 7: From an integral equation corresponding to the differential equation d²y dx² dy - sin x- +exy = x…

A: What is Integral Equation: Like differential equation, there is also integral equation. In integral…

Q: 9. The differential equation (3y cosx+4xe" + 2x'e' dx + 3(sin x +1)dy=0 is exact because aN

A:

Q: Given the non-exact differential equation (ysin(x) + cos(x) )dx + (x+y)sin(x)dy = 0. Find the…

A:

Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: Given differential equation:(tanx)dy-(4ylny-ytan3x)sec2xdx=0To find: General solution of the…

Q: 3. (cosy + ycosx)dx + (sinx – xsiny)dy = 0

A: Given: cosy +ycosxdx +sinx-xsinydy =0 ⇒cosydx +ycosxdx +sinxdy-xsinydy =0

Q: 4. What is the integrating factor of the first-order linear differential equation below? (y – 1) sin…

A: The general form of linear groupntial equation of first order is, dydx+P(x)y=Q(x)

Q: What is the integrating factor for the linear differential equation xy' – 2y = x?

A:

Q: Use separation of variables to find the general implicit solution to the differential equation. 4…

A: Given that:  4dydθ = ey sin2θy sec(θ) So, by using variable separable, we getyey dy = 14. sin2θ…

Q: From the differential equation by eliminating the arbitary constants A and B from the equation…

A:

Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: We will convert given differential equation into linear differential equation by appropriate…

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.