2. Use the underermined coefficients method to find the goneal Scution of the differential equention: Y -4y' +5y =Sinx

Q: xydy – (y 3x2) dx = 0 –

A:

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) . y'…

A:

Q: Using the substitutions 2= sin y and dz=cos y dy, the differential equation (3sin y – 5x)dx +2x² cot…

A:

Q: let (xeyx + y) dx – x dy=0 which is a homogeneous differential equation

A: Given homogeneous differential equationxeyx+ydx-xdy=0We solve this equation by substitution…

Q: Obtain the particular solution for the following set of differential equa dy = (4x2 + 7xy +2y²)dx;…

A: Given that: x2dy=(4x2+7xy+2y2)dx        and when x=2, y=0

Q: Find the general soiution of the given differential equation using Method of Undetermined…

A:

Q: Show that the solution, of the differential 5x3 is of у — ху? — х*у dy equation: dx xy² – x²y – 2r³…

A:

Q: Solve the differential equatons x(2y + In ax) dy + (x+y)dx when x=3 y=Ź y= 2 1.

A:

Q: This nonlinear differential equation, which describes wave mo- tion on shallow water surfaces, is…

A:

Q: Provided the integrating factor (IF) = xy2, find the general soution of the differential equation…

A: Multiply the integrating factor in the differential equation to make it exact.

Q: Find the values of the constant r so that y = e™* satisfies the differential equation 2y" + y' — у…

A:

Q: show that 2 = ar²+by ³ and z = ax³ + bx²y + cxy² + dy give 4 same differential rise to the egn.…

A: Introduction: When a multi-variable function is provided, one can for a partial differential…

Q: The differential equation y²x + 2y'eª = 0 is Select one: Linear Exact Seperable Homogeneous

A:

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A: Here we find the first order differential equation of given function.

Q: What is the integrating factor to (2y2 + 3xy – 2y +6x) dx + x (x + 2y – 1) dy = 0, to make it an…

A:

Q: solution of the following nonhomogeneous differential y" – 2y' +y = 4x² + e* %3D ned coefficients…

A:

Q: Find the general iné egral of the partial differential equation dz he which contains the circles +y…

A:

Q: 5. Verify that y(x) = Vx+C is a solution of the differential dy dx 1 for every constant C. equation…

A: The differential equation is given as dydx=12y2ydy=1dx

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) .…

A: Given equation is

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) .…

A:

Q: 6) Solve the homogeneous differential x2 + y? dy quation dx 2xy

A: on solving this we get

Q: Consider the differential equation x²y " – xy ' + y = 0. Given that y(1) = 2 and y '(1) = 3,…

A:

Q: Find The complete Solution of the differential eqution y" +24+4y=cosx Subjected to The condition…

A:

Q: If y(x) satisfies the differential equation y" + x²y = 0, where y(0) = yo and y'(0) = y, show that…

A: since we know that L[y''] = p2Y(s)-py(0)-y(0)

Q: y" – 4y' – 12y = sin(3t)

A: Consider the given diff. equation   y" - 4y - 12y = sin (3t) ----(1)   Associated homogeneous…

Q: dy Write down a differential equation of the form dt all other solutions diverge from y = 4 as t →∞.…

A:

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) . x"…

A: Provided differential equation is a homogeneous linear differential equation with constant…

Q: Suppose that x = 0 is a regular singular point of the differential equation %3D 2x?y"- xy' + (1+x)y…

A:

Q: (b) Find the general solútion of the differential equation d'y dy 2 +y x+1 dx - dx2 without using…

A:

Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? (A…

A:

Q: The differential equation (3ycosx+ 4.xe* +2x'e" dx+ 3(sin x+1)dy 0 is exact because OM ON Ox

A:

Q: Find the Fourier series solution to the differential equation y′′+2y=3x with the boundary conditions…

A: We will use the Fourier sine series for representation of the non-homogeneous solution to satisfy…

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) . y"…

A:

Q: The solution of the differential equation using Laplace transform y +16y 0; y (0)=6, y(0)=4.…

A:

Q: Q.4 Consider the differential equation (2y-2)y=2x-1.

A:

Q: Obtain the differential equation of the family of straight lines with slope and y-intercept equal.…

A: Differential equations

Q: Obtain the general solution of the following Second order equation by using the method of…

A:

Q: Consider P(D)y = 0. What conditions on the rootsof the auxiliary equation would guarantee that…

A: Solution: Consider the given Differential Equation P(D)y = 0 Let the Auxiliary Equation of given DE…

Q: Is the function p(x, y) = sin? (xy²) a solution to the partial differential equation + (2x + y)(2y)…

A: Use 2sinxcosx=sin2x And put the given solution on both sides we get both sides are equal  And…

Q: For x € 0,, What is the particular solution of the differential equation (y + ysinx)y' = /cos?x –…

A:

Q: Show that the coefficients of the given differential equation are homogencous and solve the given…

A: Given, The differentiating equation  x2+2y2dxdy=xy   and  y-1=1 We have to show the coefficient of…

Q: The general solution for the flowing differential cquation is * (3x+ycosx) dx +(sinx-4y )dy =0

A: We will split the equation into separate differential forms and then integrate accordingly to get…

Q: 4. Given that x=0 when y = 8, show that the general solution of the differential dy equation (x +4)…

A:

Q: Evaluate the curve f(x, y) = 0 which passes through the point (0,4) and satisfies the differential…

A:

Q: Consider the differential equation y = x+ y. Use Euler's method with Ax = 0.1 to estimate y when x =…

A: Let fx,y=x+y. Substitute 0 for n, 0.1 for h, -1 for x0 and 0 for y0 in the Euler's formula…

Q: Solve for the general solition of the followimg differential equation using FOLDE or FOBDE. 3. dy/dx…

A:

Q: Find the general solution of the differential eguation dy +y= Xe^ Sin x dx 2. dx?

A: given that,  (D2-2D+1)y=xexsin(x)

Q: Is the differential equation y sin 4x dx + x cos 9y dy = 0 exact? %3D Choose the most appropriate…

A: A Diffrentaial equation in the form :-  M( x, y)dx + N(x, y) dy = 0 is an exact  if,   ∂M/∂y =…

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.