Write the linear differential equation x²dy – (2xy + x – 1)dx = 0 in standard form dy + yP(x) = Q(x). %3D dx (1) + y (E) = + (3) + y (-) = ! dx dx (2) + y () = - (4) + y(-) + y (-÷) 1 1 1 = --- dx x2 dx x2

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: The solution of the differential equation (xy – y²)dx – (x² +y²)dy = 0 is : A) 2 In + 1|- tn -;…

A:

Q: %3D 2. ne 3० - ५

A: Discriminant of PDE of the form A∂2u∂x2+B∂2u∂x∂y+C∂2u∂y2+D∂u∂x+E∂u∂y+Fu=0 is given by  D=B2-4AC…

Q: 4. The standard form of the first order linear differential equation x'y'+xy + 2 = 0 is

A:

Q: The solution of the differential equation In(y')=2x-y is given by

A:

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

A: topic - differential equation

Q: 3. Show that the differential equation dx is homogenous. Zxy

A:

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

A:

Q: What is the general solution to the differential equation (2x- 2y- 3)dx (2x*- 4y-2)dy?

A: We have to solve the given 1st order differential equation.

Q: 3. Form the partial differential equation by eliminating the arbitrary constants a and b from z =…

A:

Q: Solve the differential equation x y' = In x-3xy with initial-value y(1) =2.

A:

Q: 2. Solve the first-order linear differential equatio a. y' + 3y = e3x

A:

Q: 5. Use a substitution to solve the nonlinear differential equation: (y + 1)y" = (y )²

A: We have to evaluate: (y(x) + 1) ( d^2 y(x))/( dx^2) = (( dy(x))/( dx))^2:Treating y as the…

Q: 1. Determine whether = is a solution of the differential equation y'--y = 0 3 y' = 6x² а. 6x2-…

A:

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: Classify the partial differential equation ´ôx² ôyôx ôy²

A:

Q: In a differential equation where y is the dependent and x is the independent variable and the…

A: In a differential equation where y is the dependent and x is the independent variable and the…

Q: Determine the form of a particular solution for each differential equation. y'' - 2y' + y =…

A: We have to determine the form of a particular solution for each differential equation.…

Q: Find the particular solution of the first-order linear differential equation        y′ + y = 6ex…

A: y'+y=6ex Comparing with y'+Py=Q, we get P=1 & Q=6ex Now the integrating factor is, IF=e∫P dx=e∫1…

Q: 5. If the characteristic equation of the differential equation 27 - 184 dx +8- y-0 is dx 27m -18m…

A: The characteristic equation of the given differential equation is 27m4-18m2+8m-1=0.

Q: Solve Partial Differential Equation: y2zp/x – xzq = y2

A: The objective is to solve the partial differential equation y2zxp-xzq=y2

Q: of the nonhomogeneous linear differential equation: у" - Зу" + 2у" 4х - 2

A:

Q: Obtain the particular solution of (3x2-2y2)y'=2xy; when x=0. y=-1

A:

Q: The General solution of differential equation def ined by: 2x² y " – x y'+y=0 is defined by y(x) =…

A: Solving Cauchy Euler differential equation

Q: Transform the given differential equation into an equivalent system of first-order differential…

A:

Q: (x^2-4x-4)(y^2+1)dx+2y(x^3-2x^2+4x-8)dy=0; when x=4,y=1

A:

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: (9x^2 + y - 1) - (4y - x)y′ = 0

A:

Q: Find the general solution of the linear partial differential equation (y + xu)p – (x + yu)q = x² –…

A: The given partial differential equation is y+xup-x+yuq=x2-y2using Lagrange's method, we…

Q: 3. Form a differential equation by eliminating the constants a and b: y = ax² + bx

A:

Q: 2) (x²y³ + y)dx + (x³y² – x)dy = o

A: (x2y3+y)dx+(x3y2-x)dy=0 this is an exact equation  M(x, y)= x2y3+y N(x, y) = x3y2-x We will evaluate…

Q: In the differential equation (2x+3y-5)dx+(3x- y-2)dy=0, the lines 2x+3y-5 =0 and 3x- y-2 =0…

A: This question can be solved using the concept of solving two linear equation.

Q: 5. (a) Find the particular solution of the differential equation x³ = 1-e²t if x(0) = 2.

A:

Q: The solution of the differential equation y^'=-2xy is a family of solutions of

A:

Q: The formation of the partial differential equation by eliminating arbitrary constants a, b from the…

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: 19. The differential equation (2xy - y^2+ y) dx + (3x^2 - 4xy + 3x) = 0 is

A:

Q: 8. The differential equation (2x' -xy² -2y+3dx-(x'y+ 2x)dy =0 is exact because ON

A: Given:     Differential equation 2x3-xy2-2y+3dx-x2y+2xdy=0 The differential equation is exact if…

Q: Choose a solution for the differential equation y'' - y = x2ex + 5: e-x(1/6x3 - 1/4 x2 + 1/4x + 3)…

A: Given non- homogeneous differential equation,y''-y=x2ex+5  ...(1). Solving the homogeneous part:…

Q: Find the general solution of the given higher-order differential equation. у" - 5у" - бу"%3D о y(x)

A:

Q: The differential equation: y²x + y² = x²yy' is solved by

A:

Q: Solve (first order linear differential equation): y'-3x2y=ex^3

A:

Q: x²u = x sin y Uyy

A:

Q: . The standard form of the first order linear differential equation x y'+xy +2 = 0 is,

A: This question is based on to form a standard first order differential equation.

Q: Discretize the differential equation y " – 3y' – y = -3t, y(-1) = 0, y(1) = 0 with step-size h %3D

A: Given: y''- y' - y =-3t, y(-1)=0 and y(1)=0 with step-size h =25

Q: 5. In the differential equation 2rydx + (y² -xy-0. what is -- 心

A: Solution

Q: What are two linearly independentsolutions of the differential equation y''-5y'-6y=0

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

Q: 1. The differential equation (x2 + y2)dx + 4xydy = 0 is Ordinary and linear Ordinary and non-linear…

A:

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

A:

Q: The particular solution of the differential equation y y- 2y = sin3x is: y(x) =Ce3x+Ce3O…

A: