3. Use Finite-Difference method to solve the boundary value problem dy dy +x dr+y= 3x² + 4x + 6 dx dx y (0) = 4, y(1)= 7. Use h=0.2 .

Q: Q2 /Find dy/dx, if: (1) x y+y =x2 (2) y = 3x* -5x' +10 у -

A:

Q: 4. (x² + y² + x) dx + xycy = 0

A:

Q: equilibrium

A:

Q: 1+x+ (x+2y)dx+(2x+3y)dy=0

A: According to the guidelines I am solving only first question

Q: Inx+ 1 dy If y = then %3D 2x3 - 3x' will be dx (2x – 3x) + 1) – (In x + 1)(6x² – 3) А. (2x³ – 3x)² -…

A: Use the formula of differentiation of fraction of Two functions in same variable.

Q: Obtain the general solution of y√(1+x^2)dx+ x√(1+ y²)dy = 0 using variable separable method.

A: solution is given below..

Q: 4) (e* + y)dx+ (2y + x)dy = 0 %3D

A: Hence, the general solution is                                            y=-x±x2-4(ex-C)2 Where C…

Q: Solve the DE (6x + y2) dx + y (2x - 3y) dy = 0. Hint: Exact O 3x^3 + xy^2 - y^3 = c O 3x^2 - xy^2 -…

A: Given differential equation:- 6x+y2dx+y2x-3ydy=0

Q: Find the general solution of dy/dx= xy-y/x^2-5x+

A: To find the general solution of the below differential equation. dydx=xy−yx2−5x+6

Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

A:

Q: Solve DE (1+e** )ax +e x/y 1 dy=0

A:

Q: solve the deq by method of substituiton

A: The given differential equation is 2x+y+4dx+x-2y-2dy=0......(1) We shall solve the differential…

Q: Find the solution of the D.E. xydx - (x2 + 3y?) dy = 0 Show your solutions on a separate sheet of…

A: Given differential equation is xydx - (x2 + 3y2)dy = 0

Q: 1. ſ f(x)f'(x) dx 2. S Vx³ dx 3. S csc?x dx

A:

Q: Solve dy (a) dx dy 1+y (b) dx 2x y+1 dy (c) (1+x 2+x dy (d) e*+y

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: [y] + √2x+3] dx = (2x+3)dy, y(-1) = O

A:

Q: d²y 2) Obtain a particular solution for d*y dx+ + + y = x³ + 2x +1 dx2

A:

Q: 5. (1-x) (dy/dx) + xy = xy". Ans. cy=(1-y)√(1-x)

A: Given equation is 1-x2dydx+xy=xy2. To find: solution of the given equation.

Q: 8. x(x² + 1)y' + 2y = (x² + 1)³

A: Given problem:- xx2+1y'+2y=x2+13

Q: - choose the correct answer If y = t^2/(t^2+1) and t= v(2x+1) the = dyldx %3D 1/N(2x+1) O 2(x+1)^2 O…

A:

Q: 46. Solve: x dy - y dx 2x^2 y^3 dy * xy^4 - 2y + cx = 0 O xy^4 - 2y + x = c x^2 y^3 + 2y + cx 0 O…

A: Topic:- differential equations

Q: 2. 3y² dy/dx-1=3x²+6ydy/dx, y(0) -1 and determine the interval of x in which the solution is…

A: To solve the given initial value problem:  3y2dxdy​−1=3x2+6ydxdy​ with the initial condition y(0) =…

Q: Solve the DE xy(y² + 1)dx + (x²y² - 2) dy; y(1). = 1 O x^2 (y^2 - 1) = 2 - 4ln(y) O x^2 (y^2 + 1) =…

A: Here we have to solve the differential equation.

Q: 2. Find all solutions: dt dy dx = 4x + y x + 4y' x > 0.

A:

Q: x²dy + (y² + 3xy + 4x²) dx = 0 when x = 2, y = 1

A: To obtain general and particular solution satisfying initial condition indicated byusing homogenous…

Q: 3. (1−x³) d²y dx² DE -+ (sin x)y' − 3xy = ln x(+1) TYPE ORDER DEGREE LINEARITY

A: Need to write down the type, order, degree and linearity of the given differential equation.

Q: Given G(x, y) = 6y²(e(²) +e (¹)), where and y are found to be In 3 and 3 with maximum possible…

A:

Q: Solve the IVP dy r(x² + 1) 4y3 y(0) dr V2

A: We are given: dydx=xx2+14y3 ⇒4y3dy=x(x2+1)dx Now, Integrating both sides,…

Q: 22. (2xy +y) dx + (x² + 2xy + y) dy= 0

A: