Solve the initial value problem: xy + y² " x² y' = y(−1) = by following the steps: Y (1) make the substitution u = 6 and simplify the X equation. Caution - calculate u' carefully!! (2) notice that the new equation is separable and solve for u (3) reverse the substitution to solve for y (4) use the initial condition to solve for the constant of integration y(x) = n(x) + 6 Note that we've been given an intial value of the form alla) h where so this only determines X

Q: Find g(x) if g (x) = (30x² – 60x) - 75»²–15z² and g(0) = -3. Round any numbers to 4 decimal places…

A: We use substitution method

Q: Find an antiderivative F(x) of the function f(x) = - 2x²5x + 2 such that F(0) = - 15. F(x) = Now,…

A: On solving this we will get

Q: Solve the initial value problem: y' + y cotx=cscx, y(π/2)= π/2.

A:

Q: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

Q: Use Exact, Then solve (1 = In(x) +)) = (1 – In(x))y`

A:

Q: Write down the auxiliary (characteristic) equation and then solve the initial value problem:…

A:

Q: Solve the following equation and find the solution y as a function of x and C (constant of…

A: We have observed that the given differential equation is a first order separable ODE. So, by…

Q: Using homogenous, solve y2+x2y = xyy

A: Given: y2+x2y = xyy'

Q: 3) y'+ 2xy = 2x3 =D2x' SOLVE

A: Given,y'+2xy=2x3This is the linear differential equation of the…

Q: Solve: x"(t) + 2x'(t) + x(t) = 3t e-t x(0) = 4, x'(0) = 2 Evaluate: F(2) = Evaluate: f(1) =…

A:

Q: Find y' and y". y' y" = y = (²+ √x)³ 3

A:

Q: 2. Solve the first order equation by using integrating factors. y' - 3y = e-2x

A:

Q: Identify f(x) to be used in variation of parameters to solve for y, e" y" + y' – 3y = x

A: To find f(x) write equation in form of y" + P y' +Q y = f(x).

Q: Solve (c) y" + 4y = 0, (d) (1+y/2)3 = (y')².

A: Solution is given below:

Q: y = xy' – y* + 1 find general solution and particular solution.

A: Given, We have to find general and particular solution for it. Working:

Q: x(y')2 - 2(y')3 - 2x - y = 0 find the general solution of the equation

A: Given differential equation is, xy'2-2y'3-2x-y=0 Let, the given equation be, y'=dydx=p Thus,…

Q: y' - 3y + 2y =0, y(1)=2, y(2)=0, h=1/4. Solve using finite difference method.

A:

Q: y' +y = x*y2 , y(2) = -1,x > 0 is

A:

Q: Find the general solution to (t² + 4)y' + 2ty = t²(t² + 4). Enter your answer as y = .... Use C to…

A:

Q: 9. For each n E IN, let Xn be the set of polynomials of degree equal to n, and let Pn = U_0 Xk. True…

A:

Q: post office sells 4-cent sheep stamps and 2-cent sunset stamps. Cole bought 5 stamps spent exactly…

A:

Q: x² + y² Solve y'= 2. xy 3. Solve (x+y-1)dy = (x-y-3)dx

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: [3 Marks] B1(b): Solve the initial value problem : f'(x) = x14 + 12x + 18 and f(0) = 7.

A: To solve the following initial value problem, f'(x)=x14+12x+18 and f(0)=7 f(0)=7 implies that when…

Q: y''- 4y'+ 4y=e2x ln|x| + e2xsinx Find the general solution of the equation

A:

Q: y' +y = x*y2 , y(2) = -1,x >0 is

A: Given, The initial value problem is,

Q: [Q3] Using the method of undetermined coefficients. (a) Solve y" - 2 y' - 3 y = 2e* -10 sin x, y(0)…

A:

Q: Of the solutions to the three di↵erential equations above which one is increasing at (1, 1)? Explain…

A:

Q: у 7. y' +²√y = 0, y(1) = 0 - x

A:

Q: y'-2 xy=2 y (0)=1

A: