Question 3 How do we determine if a differential equation M(x, y)da + N(x, y)dy = 0 is an exact differential equation? A differential equation is exact if: әM aN Әx ду әM ƏN ду Әх әм ду = 0 and әм дх - = = 0 and - ON ду Submit Question ƏN Әх = 0 = 0

Q: What is the general form and standard form of exact differential equations?

A: Differential equation: A equation is that the linear combination of the variable quantity and…

Q: dP 17. = P – P dt

A:

Q: Question 3 Use Laplace transform technique to solve the initial value problem y + 4y = g(t), y(0) =…

A: First write the unit step function for the given piecewise function gt.

Q: x²y' + y? + 2x - xy' = 2xy +y

A: Given: x2y'+y2+2x-xy'=2xy+y rewrite this equation , we get y-2xy-1dx+x2-xy2-2y+1dy=0…

Q: A differential equation, a point, and a slope are given in photo. Sketch two approximate solutions,…

A: Given differential equation is dydx=24-x2 Point :- 2, π Slope Field:-

Q: Example: Solve the DE y" – (1+ x)y = 0

A: See the attachment.

Q: Determine whether the differential equation (3x+5) + (3y — 3)y' = 0 is exact. If it is exact, find…

A:

Q: Exercises. Find the general solution, and if an initial value is given, solve the IVP: (2) y" + 8y'…

A: As per our guideline we are allowed to do 1 question at a time . Please post other questions next…

Q: (4r + 5)2 2- + tanzy= dr COSI

A:

Q: 9. cos(xy) (x dy + y dx) = 0; y(1) = = 10. [y sec2 (xy) + 1) dx + x sec (xy) dy = 0; y (;) =" %3D 3.

A:

Q: Check that the differential equation is linear and find the general solution Y'-(6/X)Y = x^4

A: Given differential equation is y'-6xy=x4 which can be written as dydx-6xy=x4. We have to check…

Q: y" + y" = 0

A:

Q: Solve the differential equation y''''+y''=3x2+sinx-2cosx a) what is the complementary solution b)…

A: We have to solve the differential equation y'''' + y'' = 3x2 + sinx - 2cosx a) Complementary…

Q: Determine all solutions of differential equation y' + ysin x = SIN 2x

A:

Q: How do I solve this differential equation using P(x), Q(x) and v(x)?

A: The given differential equation is,

Q: (cos y+ y.cosx-ec*.sin x)dx+(sin x – xsin y)dy =0 cos.x

A:

Q: y" + 25y = 5 tan²(5x) cos(5x)

A: To Determine :-  The second order differential equation : y'' + 25y = 5 tan2  5x cos  5x

Q: In which form first-order linear differential equation can be written ?

A: A general first-order differential equation is given by the expression dydx+Pxy=Qx, where Px and Qx…

Q: Use substitution to find a general solution of the differential equation  a)  x^3*y'+x^2*y=y^2…

A: We need to convert Bernoulli equation into linear differential equation form by using substitution

Q: Solve differential equation by variation of parameters y"+9y = sin?(3x)

A:

Q: Fond Particular Solution of the Lifferential equation 13 Y = 6 (²53x - 8 1 Y"+ 4y¹ + Yo 85in3x y (0]…

A: We have to find the particular solution of the differential equation y'' + 4y' + 13y = 6 cos3x - 8…

Q: Solve (D² + 4D + 5) = 0 ,y(0) = 1 ,y'(0) = 0. %3D

A: Differential equation