뿜= 3) consider the differential equation dy = (Y²_9) (y + 7) ² (x²79)(y-7) a) sketch its phase line portrait (used filled in dot for Stationary. Identify points where it has no solution - indicate with (solations) a cohole. Identify its stationary points & classify each as as being stable, unstable or semi-stable. b) For each stationary point, identify the set of intial values. yet) will converge to the Y() such that the solution. point as

Q: Identify the first order DE and show the solution for (x-x^3ye^-2y)dy-dx=0

A: Given the differential equation

Q: What is the order of the differential equation representing the family of ellipses having center at…

A: We will find out the required value.

Q: A particular curve passes through (1, 1) and satisfies the differ- ntial equation dx = (1-3y²³) dy.…

A: Let's find equation of curve in the form of x=h(y).

Q: 2. Reduce to an exact equation and solve it: dy_2xsin 2 y+(2siny)/x² dx 2x²cosx-(2cosy)/x (2x²ysin…

A: GIVEN: dydx=2xsin2y+(2 siny)/x22x2cosx-(2cosy)/x             (2x2y siny -x y3sinx)dx +(x3siny +x3 y…

Q: 4. Find d?y/dx² for the following functions: b) y = cos*(sec² 3x)

A:

Q: 2) Find the derivatives of a) y = 7 - 6x-x² b) y - ³x 8 √x

A: Given :(a)y=7-6x-x2(b)y=-8x

Q: c. y" +4y=tan2x %3D

A: Solution of the given differntial equation is

Q: Solve by lagrange method, find the general solution to the ODE y = x(y' - x cos(x))

A: Given differential equation is  y=xy'-xcosx⇒y'=xcosx+yx⇒y'-1xy=xcosx which is of the form y'+Py=Q.…

Q: Consider the differential equation: y'=t(y² + 1)

A:

Q: find the differential equation of the family of ellipses having a center at (1, -2), major axis is…

A:

Q: Solve the IVP (1/x + 2y^2x)dx + (2yx^2 - cos(y))dy = 0, y(1) = pi. Give an implicit solution.

A: Consider the differential equation 1x+2y2xdx+2yx2−cosydy=0.........(1) Compare the equation (1) with…

Q: solve the bernoulli equation dy/dx+y = y^2(sinx+cosx). and show that the answer is y(cosx+Ce^x)=1

A:

Q: y′= (6xe^(6x)) X (cos^(2) (6y)) a) Write the equation in an integrable form by separating it into…

A: Solve using variable separable method.

Q: Solve the HDE: z'y = ry+3xev*. Your Answer:

A: To solve the homogenous differential equation given.

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: Let c be a real number. By taking the necessary derivatives, show that the function f(x,t)= ln(x+ct)…

A: The given function is

Q: Find stationary points of y = cos (4nt)

A: given function is

Q: Find the order and the degree of the differential equation cos x COS X A 2,4 B) 5, 8 © 5,4 5,2

A:

Q: classify by type, order and linearity the following equation (1-x)y"-8xy'+6=cosx

A:

Q: Solve the following 3rd order equation: y'"+2y"-y'-2y=0

A: First find roots then general solution..

Q: 11. y = (x + y) 12. y =x sin -1x + 1 – x2

A: Let's find.

Q: y = eVx+cosx

A: To  findderivative of1)y=ex2+cosx

Q: Solve to Find if cscx – San () dt = 4 – y?

A:

Q: 6) y = (sin¬1 8t) (sec -1 derive

A: First, we use the product rule

Q: Find dx (e3t + 1)dt. -cos(3rx)

A: