d²y dy + 9y = 0 dx

Q: Find the general solution of the equation x(y2 + 1)dx + (1+ x²)dy = 0. A. In(x2 + 1) + 2Arctan y = c…

A: The given equation is; x(y2+1)dx + (1+x2)dy =0

Q: 5. Find the general solution of the given DE: 2x + 2xy2 y + 2x?y dy dx

A: First We will separate X and y terms of the given differential equation and than integration gives…

Q: Solve the particular solution of the given DE: x(r^3-xy^2+2y^3 )dy-y(r^3+2y^3 )dx=D0 @r=1, y=1.

A: We have to solve given problem:

Q: Solve for the general solution of the given non-exact DE. y(2x + y?)dx + x(y² – x)dy = 0

A: The given differential equation:y2x+y2dx + xy2-xdy=0We need to solve the above equation.

Q: (x + y) dx + (3x + 3y - 4) dy = 0

A: given differential equation  x+ydx+3x+3y-4dy=0 solution let y+x=u differentiate dy=du-dx…

Q: Find the solution to the DE. (y- x+ xycotx)dx + xdy=0

A:

Q: dx dt dy dt х — 2у + t х — у + 2t

A: The given equation is dxdt=x-2y+tdydt=x-y+2t This equation can be rewritten as x'=x-2y+t t=x'-x+2y…

Q: Obtain the general solution of the following equations. 3. (4xy + 3y²)dx + x(x + 2y)dy = 0

A:

Q: Reduce the given DE into Bernoulli's equation: - 2x*y¬ dx 3 y-4 dy_ y5 2x4 y4 dy dx dx 3 3 dy 2x* у…

A:

Q: Find the general solution of the given Attached equation

A:

Q: Find the general solution of the given Attached equation

A:

Q: Given the initial condition y(0) = 1, find the particular solution of the equation

A:

Q: Find the general solution to the following equations: dy у-х dx y+x

A:

Q: Find the general solution of the given Attached equation

A: Given: differential equation, To solve the differential equation first, substitute

Q: Find the general solution of the given Attached equation

A:

Q: d.) (y³ + x ln ) dy + (y In ) dx = 0

A: we have to find

Q: B) Find the general solution to the following DE. dy y? + x2 = 0 dx

A: Given differential equation is y2+x2 dydx=0

Q: (xy)dx + e*dy = 0, as xo, y =D;

A: Given:- (xy2) dx + ex dy=0 To find:- Particular solution of given differential equation

Q: dy e I+ x + ×y +メ dx

A:

Q: solve by Bernoulli's Equation y(6y2 – x - 1) dx + 2 x dy = 0

A: Given differential equation is  y(6y2-x-1) dx + 2x dy=0 ⇒            2x dy = - y(6y2-x-1) dx…

Q: The trial solution for the non-homogeneous equation d²y +3. dx? dy – 4y = (x³ + x)e* is %3D dx

A: Trial solution: - Assume the differential equation's right side, f(x), is a linear combination of…

Q: Solve the Euler equation d²y dy 3x? dx -5у%3D0 +x dx given that y(1) =1 and y'(1) = 2.

A:

Q: (2xy +y) dx + (x²- x ) dy = 0

A:

Q: The point of intersection when the coefficients of dx/dy are equated to zero of the given DE:…

A:

Q: Find the general solution of the given Attached equation

A: Differential eq:9d2ydx2+6dydx+y=0The auxiliary eq is 9m2+6m+1=0

Q: Solve the given initial-value problem. dy 3D х+ 4y, у(0) %3D 6 dx y(x) =

A: Given that dydx=x+4y , and y(0)=6We need to find the solution of above differential equation.

Q: Solve for the general solution of the given non-exact DE. (2y2 + 3xy – 2y +6x)dx + x(x + 2y – 1)dy =…

A:

Q: 2. (y + 1)dx + (4x – y)dy = 0

A:

Q: 2. 2x5 = y(3x* + y²) %3D dx

A:

Q: d²y dy +4 dx² + 4y = 0, when x = 0, y = 1, y' = -1 dx

A:

Q: Given: dy/dx = (4x^2 – 7x) / (3y^2 + 2). Find the particular solution at x = 1, y = 1

A: Here

Q: Solve the general solution of the given DE:(2r+y)dx-xdy=D0*

A:

Q: S.2 „Determine whether the equation (3x + 2y)dx + (2x + y)dy = 0 is exact. Find the solution if it…

A: Given that  (3x+2y)dx+(2x+y)dy=0 To determine the general solution

Q: Solve the D.E  dy/dx=2exy3 , given that y(0) =1/2

A:

Q: 3. Show that the equation (x²y)dx + () dy = 0 is exact and then solve it.

A:

Q: Obtain the general solution to the equation. dy y dx X + 9x + 7 The general solution is y(x)=,…

A:

Q: What is the general solution to the following equation: (dy/dx)= (y/x)+6x+1

A: Compare the given differential equation with standard form and calculate the integrating factor (IF)…

Q: 2. Determine y so that it will satisfy the equation: d'y_dy dx = 4e* +3e²* dx with conditions y(0) =…

A:

Q: Find the general solution of the equations given below: dy i) 4 - y = x² – 3x; dx2

A:

Q: solve the differential equation with the given initial condition.

A: Given:  The differential equation .

Q: Solve the DE by Bernoulli's Equation 3 1.6 y² dx - x (2 x³+ y) dy = 0

A:

Q: 3. Choose one of the following first-order equations to solve. dy (x² + 1): + 3x(y – 1) = 0 dx а. %D

A:

Q: find the general solution of the given equation. d2y/dx2 + 4 dy/dx + 4y = 0

A: d2ydx2+4dydx+4y=0 The auxiliary equation is, r2+4r+4=0⇒r+22=0⇒r=-2

Q: d²y dx² - dy 4 + 7y=0 dx

A:

Q: xy dx + e'y? - 1)dy = 0

A:

Q: find the general solution of the given equation. d2y/dx2 - 6 dy/dx + 9y = 0

A: Given: d2ydx2-6dydx+9y=0 Now plug dydx=D ⇒D2-6D+9y=0 Its auxiliary equation is,…

Q: Find the solution of the equation dy -y = x dx | subject to the condition y(1) = 2. %3D

A: Given differential equation is xdydx-y=x and y(1)=2

Q: Solve xy( 1 + x y? ) = 1 by using Bernoulli's equation. %3D dx

A:

Q: Find the general solution of D.E. below: (x-2y) dx + (2x+y) dy = 0

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.