3) Solve. dy e*y dx = e-y + e-2x-y (2y + 2) dy – (4x³ + 6x) dx = 0, y(0) = –3. dy + y = f(x), y(0) = 1, where dx 01 Graph the solution for this DE.

Q: 3.) (2xy³ + y4)dx - (2y - y³x)dy=0

A:

Q: d²y Solve the particular solution for = 2 – 4x when points (0, 2) and (-1, 3) are on the dx2 curve.

A:

Q: (d) What can you say about the graph of y = 4(x) for x>x*? (e) Verify that y = x – 1 is a solution…

A:

Q: (D 3)²y = e*.. %3D

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: (D² +1)y = sec x. %3D

A:

Q: dy = 12x2 – 7eI 5) Find the equation of the curve that passes through (0, 9) if its slope is given…

A:

Q: (16x + 5y)dx + (3x + y)dy = 0 the curve to pass through the point (1,–3) %3D

A: The solution of the problem is given in the next steps.

Q: Given the Bernoulli's equation Dy/DX+yP(x)=y^n Q(x) and x=y^1-n, reduce the equation to the linear…

A: Given differential equation is                                           dydx+yP(x)=ynQ(x);  x=y1-n…

Q: What is the function of the graph? Select the correct answer. Oy-x? - 82? + 5x Oy-6x-8x3 + 5x y-x° -…

A: Facts : 1. Complex roots always occur in conjugate pair. 2. If the polynomial has degree 'n' : A. n…

Q: 2²ye+v°-²dx dy dz 1 -1

A: We have to calculate the integral.

Q: (а) Consider the following equation: xy dy – (3x² + 4y²) dx = 0 | (1) State the order of the…

A: Questions from differential equations.

Q: Find and classify the stationary points of the function 1 G(x, y) = 3x² + xy - 2y² - 2x + 4y - 1

A: Given function is .For stationary points .Now, or, And or, To eliminate y from (1) and (2),…

Q: dy_ sec²y 1- 1+x² 2 when x=0 O y=

A:

Q: A linear model of the spread of an epidemic in a community of 1000 people is the equation: dx/dt =…

A: To find the number of people x(t) who have contracted the disease at the time oftime t.

Q: (b) Solve the equation 2 = dy %3D -x+/x²+yz y(-3) = 4 for -3 <x57 taking the dx y step-length h =…

A:

Q: 6p sin oa, + 1.5pcos oa C/m², evaluate both sides of the divergence theorem for the region bounded…

A: Solution :-

Q: 14. (6x3y + 2) dx - (2x - y - 1) dy = 0. ANS. 3

A:

Q: 2. Separation of Variables:Solve the equation (1 + y² ) dx + (1 + x² ) dy = 0 , if x = 0, y = -1

A:

Q: Trace the curve y? = (x - 1)(2x + 3)(3x – 1). %3D

A: Trace the curve y2=(x-1)(2x+3)(3x-1)

Q: dy 3(x+y+1)2-(x +y- 1)² dx

A: Given :

Q: Sketch the graph of  2x=3y−22x=3y−2.

A:

Q: 7. (x+2yXdx- dy) = dx + dy. %3D

A:

Q: (D+1)2 y=e-x sec2 xtanx

A: Given that, (D+1)2y=e-xsec2xtanx Now the equation can be written  as,…

Q: Find the solution. (dy/dx) + xy = xy³ A x = (ce-²-1) By = (ce²+1) 7² y = (ce x²-1) x = (ce)² + 1) ²…

A: We have given a differential equation ,  dydx + xy = xy3 Multiply throughout by dx ,  dy + xy dx =…

Q: 1.² T 20 40x-x² 9√x²+y2 dydx=

A: We have to solve ∫020∫x40-x29x2+y2dydxThe region bounded by0≤x≤20x≤y≤40x-x2⇒x=y and y=40x-x2squaring…