The differential equation X dx + y dy= xy² dx can be rewritten as y + p(x)y=Dq(x)y" . The solution can be written in the f) – g(x) is? form f(y) = 1+ Cęgwx) ", where C is an arbitrary constant. Then y-x А) у-х y+x ху+x D) ху+1

Q: The solution of the differential equation 3.9 + x² + x²y+ 3.9y 1+ Y dy dx using variable separable y…

A: The given equation is dydx=3.9+x2+x2y+3.9y1+y On simplifying this, we get…

Q: Show that the first order differential equation (x + 1) y' - 3y = (x + 1)5 is of the linear type.…

A: To solve x+1y'-3y=x+15; y=1.5 when x=0

Q: Show that the differential equation  (2xy3 - 3y2 + 2xy2)dx + (3x2y2 - 6xy + 2x2y)dy = 0 is exact and…

A: To show that the differential equation  2xy3-3y2+2xy2dx+3x2y2-6xy+2x2ydy=0 is exact and to find its…

Q: show that y2 = Cx + (1/8) C3   is a solution to the differential equation y= 2xy' + y2 (y')3

A: y2=Cx+C38and given ODE is:y=2xy'+y2(y')3

Q: 20.Find the particular solution of the differential equation x (+1) - x-2y, given x -1 when y = 3

A:

Q: The general solution of the homogeneous differential equation 3x y" + 7xy + y = 0 can be written as…

A:

Q: Eliminate the arbitrary constants of Ax^2 + Bx +Cy^2 - Dy = 0 (where A, B, C and D are the…

A:

Q: What is the particular solution to the differential equation (1-xy)? + (y² + (1-xy)- )dy = 0 and y =…

A: Givendx1-xy2 + y2 + x21-xy2dy = 0withy(4) = 1

Q: A firm hires 3t% workers each year but loses 5% each year due to retirement and poaching from…

A: topic - differential equation

Q: 6) ( y - 2xy ) dx + 3x'dy - 0 ; y( 2) = -1

A:

Q: Give the general solution of the differential equation -5x y"+ 10y'+ 25 y =3xe a) O y=C, e*+ C,xe…

A:

Q: Find the solution to the linear system of differential equations x' = -11x – 36y, y = 3x + 10y,…

A: we will find the general solution of the linear system of differential equations by finding the…

Q: For the differential equation (x² – 4)y" + (x – 2)y' + 2y= 0, the singular points are: %3| x=2 and…

A:

Q: (2) The particular solution y,(x) to the differential equation y" + 100y = sec2 (10x) is of the %3D…

A: Given y"+100y=Sec2(10x) ---1Compairing with y"+q(x)y'+r(x)y=g(x).Auxilliary equation corresponding…

Q: What is the particular solution to the differential equation x(x³ – xy² + 2y³)dy – y(x³ + 2y³)dx = 0…

A:

Q: Find the particular solution of the first-order linear differential equation     y′ + (1/x)y = 0for…

A: y/+1xy=0 On simplification, we get ⇒dydx=-yx⇒dyy=-dxx Now integrating on both sides, we get…

Q: One solution of the differential equation y''+y'=0 is y=e^-x. A second linearly independent solution…

A: We will find out the required solution.

Q: Two linearly independent solutions of the differential equation y" + 2y' + 4y = 0 are Select one: O…

A: We have to find linearly independent solution of given differential equation.

Q: 3. Show that the differential equation (1 – 2y + x In a)dx + (e2v – 2x)dy = 0 is exact and find its…

A:

Q: 8. Consider the homogeneous linear equation: 2.a²y" + 3xy' – y = 0, x > 0. (a) Explain why y = e" is…

A: Note: Since these are independent subparts, according to our policy we are only allowed to solve…

Q: Find the solution of the differential equation x In x = y(1+ /3 + y2 )y' that satisfies the initial…

A:

Q: 2. Solve the differential equation (3.x² – x³ + 3y – 3.xy – y³)dx + 3(x + y²)dy= 0, - by determining…

A: Exact differential equations solved by using integrating factor

Q: Solve the differential equation (3xy+y2)+(x2+xy)y′=0 using the integrating factor μ(x, y) = (xy(2x +…

A: The differential equation is 3xy+y2+x2+xyy'=0.

Q: 2. Find the differential equations by eliminating the arbitrary constants of a) y = C₁x + 2² b) y ex…

A:

Q: The general solution of the homogeneous differential equation 4x'y" + 9xy' + y = 0 can be written as…

A: Solution of the given Differential Equation

Q: 5. Show that if u is any solution to the differential equation y" = -y then u² + (u')² is a…

A: See below the solution

Q: Please, reply as soon as posible! Determine the general solution of the differential equation y ′ ′…

A: To find its general solution for the below differential equation. y''−16ky'+64k2y=ex

Q: If yy of a differential equation is ce2x + Cze3x + cze-3x, then W = (a) 0 (b) (c) 5e-* (d) e5x d O a…

A:

Q: 9. What is the particular solution of the linear differential equation ,3 Y = x° – 2xy; when x = 1,…

A:

Q: If the auxiliary equation associated with a homogeneous linear differential equation with constant…

A:

Q: Solve the differential equation by separation of variables: (x²+4) dy + x²y²dx=0 Ⓒ 1 y There is no…

A:

Q: y=Aexp(Bx)+Fexp(Gx) is the particular solution of the second order linear differential equation:…

A:

Q: Which term is included in the solution of the differential equation y” - 2y’ - 3y = e^x , y(0) = 1,…

A: Given differential equation y” - 2y’ - 3y = e^x , y(0) = 1, y’(0) = 1

Q: 5) Verify that y = 2e3 – 2x – 2 is a solution to the differential equation y' – 3y = 6x + 4. - -

A: Given that y=2e3x-2x-2    ......(1) Differentiating (1) with respect to x: y'=6e3x-2…

Q: Show that: a) The price of the stock itself, that is when u(t, X1) = X1, solves the…

A:

Q: Find the particular solution of the differential equation y’ + 7x = 0, at y = 0, x = 3. y = 63x2/2 y…

A:

Q: Find the general solution of the first-order linear differential equation y′ + 3x2y = 6x2 for x >…

A: Given: The first-order linear differential equation: y'+3x2y=6x2 for x>0.

Q: Two linearly independent solutions of the differential equation y" + 2y' + 4y = 0 are Select one: O…

A:

Q: Show that y = ce* + (x + 2)e²x is a general solution for the differential equation y' - y = (x +…

A:

Q: The general solution of the differential equation x²y" – 2y = Inx² is C1x=² + c2x – ln x – , O C1x²…

A: The solution is given as

Q: Find the general solution of the differential equation y"+ 81y = 7csc9x. 7 7 A. y = C1 cos9x + C2…

A:

Q: Which one is the fourth order differential equation whose solutions are  e^(3x),e^(−3x) and  xe^(2x)…

A: We will use basic of ode.

Q: The differential equation formed by eliminating arbitrary constants a ,b and c: y= ax³ + bx+ cx +7…

A: y = ax³ + bx + cx + 7 So, y' = 3ax² + b + c  So, y" = 6ax  So, y''' = 6a

Q: Determine the solution of the differential equation у"+2y" - 5y - бу%3D0 that has values y= 3, y = 6…

A: The differential equation y'''+2y''-5y'-6y=0 where y0=3,y'0=6,y''0=12. Rewrite the equation using…

Q: The solution of the differential equation by variable separable method dy 3 + y?) (3x² + 6) is_ dx…

A:

Q: Find the general solution of the higher order linear ordinary differential equation: y"' + 2y" + 4'…

A: We have to find general solution of given differential equation.

Q: The differential equation (2x' - xy - 2y+3 dx- (x²y+2xdy = 0 is exact because OM ON

A:

Q: The General solution of the differential equation 3x2 + 2x + 6 is x3 + x2 + 6x dy using variable…

A:

Q: Form the differential equation if its solution is y=acos2x+bsin2x a. y"+4y=0 b. y" – 4y = 0 c.…

A:

Q: 7. Find the particular solution of the differential equation dx 5x³y = x³ passing through the point…

A: The given question has been solved in detail

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.