Given a family of circles x2 + y2 – 2Ax – 2By + C The associated differential equation is [a + (y')?]y" + by'(y")²Q 0 Then a -b =

Q: 3. Solve for y in the equation y = e* sin x + e* cos x - y +c

A: the given equation is y = ex sinx + ex cosx - y +c

Q: For which of the following equations the functions yı (t) = cos(2t) and Y2 (t) = sin(2t)

A:

Q: 8. Show that the function y = ex (sin 2x + cos 2x) is a solution of the equation y" — 2y' + 5y = 0.

A: The given function is; y=ex(sin2x+cos2x) And the given equation is; y''-2y'+5y=0.

Q: 6. Find Sin 5x (b) y = THcos 5x dx

A:

Q: Find all singular points of the given equation and determine whether each one is regular or…

A:

Q: Find indicial equation at each regular singular point of 2.x (1+x) y" + (3+ x) y' – xy = 0.

A: The given equation can be written as:

Q: Find a particular solution yp for the equation. y" - 6y' + 5y = cos3x 3sin3x

A: Consider a non-homogeneous differential equation of the form a(x)y''+b(x)y'+c(x)y=r(x). Then the…

Q: 3. y'-2xy = x² + y² { y=tan(x+c)-x}

A: The given differential equation is

Q: 2. Draw the graph z = - cos(y) for 0 < y < 2n, and then use it to help you sketch solutions of y' =…

A: Firstly we draw the graph of z=-cos(y) for the given interval. Then we find the critical points and…