Determine the largest interval containing r = 0 for which the initial value problem (r – 1)y" + [tan(x)]y' + 3y = e², y(0) = 1, y'(0) = 2 %3D ould have a unique solution.

Q: Find the general solution valid near x=0 (x2 + 4) y" + 2xy' -12y = 0

A: We have to solve given problem:

Q: The solution of y" – 3y' + 2y = 0 with initial conditions y(0) = 1 and y'(0) = 0 is given by?

A: y''-3y'+2y=0The initial condition are y0=1 and y'0=0

Q: x²y" − x(x + 2)y' + (x + 2)y = 0, 0 < x

A:

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: Find a continous solution satisfying the equation and the initial condition (1+x²)y/ +2.ry = P(x) r,…

A: we have given a first order differential equation with piecewise function P(x) we need to find a…

Q: y' cos x + y sin x = 2cos³x sin x- 1 What is the particular solution when y(T/4)=3v2 ?

A: Given differential equation is y'cosx+ysinx=2cos3xsinx-1 we have to find the particular solution…

Q: Obtain two linearly independent solutions valid near x = 0  xy" + x(x - 1)y' + (1 - x)y = 0

A:

Q: Use variation of parameters to find a particular solution of y"- 2y' +y = 14xie" Yp(x)

A: y''-2y'+y=14x32ex find the roots for the homogeneous system  r2-2r+1=0 r-12=0 r-1=0 r=1 for one real…

Q: y" + 3y' + 2y = cos(e).

A:

Q: Solve the IVP 2y"+5y'-3y=0 y(0)=-5 y'(0)=29 y(x)=?

A: The given differential equation is                                                   2y''+5y'-3y=0…

Q: Find the solution of y" – 2y' + y = 36 et with y(0) 6 and y' (0) = 5.

A: Given

Q: Can you give the interval of the solution as a Bernoulli Equation?  y(0)=1 ie...  y'+p(x)y=g(x)y^n…

A:

Q: Find the solution of y' + p(x) = 4x if y(0) = 3 and where

A:

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: 8. (y – In æ) dæ + (x +1) dy = 0, y(1) = 10 Ghenoral Form : y' + Pixly= Q(x) I (x): PLk) du : Final…

A:

Q: xy' + 2y = 3x, y(1) = 5 %3D

A:

Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

Q: Order | Degree Indepenc ependen Partial Linear Variable Variable y' = x +óy y" = 4y +y3 (d²y' \dx² +…

A: Note: Ordinary differential equation: An differential equation which involves dependent variable,…

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: y" + y = 0, y(0) = 0, y' (5) = 2

A:

Q: y" + y = sec (x)

A:

Q: 2) Find a general solution to the following Cauchy-Euler equation for t > 0. (t^2)y"+3ty'+10y=0

A: Given: Here, the given details are, The given equation is, t2y''+3ty'+10y=0. To find a general…

Q: Find all solutions of the following differential equations: (a +1)ry/ – (d + 1)y= cos y/x a=1, b=6,…

A: Given: a+1xy'-d+1y=cosyx For, a=1, d=6. We have, 2xy'-7y=cosyx …1

Q: y" – y' = sin(t) y(0) = 1 y' (0) = -1

A: We have to solve the IVP           y''-y'=sinty0=1y'0=-1

Q: (1+x2) y' + 2xy - 4x2y3 = 0 (Bernoulli)

A:

Q: If x²y + y²x = 6, then find y' at x = 2.

A: