Q. Solve the equation using Variation of Parameters: y" – 5y' + 4y = x. -

Q: The differential of y = (5x-6)e2z has the form | dy = (mx + b)e2# dz %3D Find the values of m and b.…

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Q: find dy/dx

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Q: Q4) find the soluation of differention equation using exact equation 1) (1 + x²)dy+(2xydx)=0

A: I am attaching image so that you understand each and every step.

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: Q.1B) Solve the follwing diferential equation: 1 dy x dx siny + ycosy 2logx +1

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Q: dz b- Solve by chain rule to determine dx z = x²y* -2y , y = sin(x²)

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Q: Q5: Solve by using Modified Euler's Method. dy = x + cos(y) ;0 <x<1 ;y(0) = 1;h = 0.5 dx

A: Given the DE is dydx=x+cosy,0≤x≤1,y0=1,h=0.5. The modified Euelr's method is defined as follows:…

Q: 7 1. 2ydx+x²dy = - dx; y = - when x =1 In 2 2

A: Given:- 2y dx +x2 dy =-dx  To find:- Solution of Differential equation at y = 7/2 when x =1/ln(2)

Q: Q5: Solve by using Modified Euler's Method. dy = x + cos(y) ; 0 < x <1 ;y(0) = 1 ; h = 0.5 dx

A: Disclaimer: We use the modified Euler's method to solve a first-order ODE and find the value of the…

Q: Q1. Solve the IVP by finding appropriate integrating factor an (x² + y² – 5)dx – (y + xy)dx = 0,…

A: Consider the given differential equation Mdx+Ndy=0 The equation is exact if ∂M∂y=∂N∂x The solution…

Q: Find an integrating factor and solve the equation у da + (3гy — e Sу) dy %3D 0. -

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Q: a) Solve etan y dx + (1+ e*) sec'y dy = 0. sin(3z + z?) b) Find y for y = (6 – z*)3

A: The given differential equations is  and the other equation is y=sin(3z+z2)6-z43 The differential…

Q: 3. Obtain the homogeneous linear equation satisfied by the following function. y = x² Sinx + e5x

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Q: FIND 2 DIFFERENT (LINEARLY INDE PENDENT) POR THE D.E. SOLUTIONS y"_x² y'- 3xy = o 2.

A: The linear homogeneous ordinary differential equation has the form pxy'' +qxy' +rxy=0. If the…

Q: b) Solve by using Runge-Kutta method to find y,. dy = x + cos(y) ; 0Sx<1 ;y(0) = 1; h = 0.5 dx

A: Solve the intial value problem, using Rung-Kutta method

Q: 2. Given that y = (a + bx)e-* where a and b are constants, show that +2 +y = 0 dx2 dx

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Q: Q. 4. Find the solution of dx -10y 4e using variation of parameter method. dx %3D

A: We have to solve given problem:

Q: The equation AT*y²-J¤+1 )dy = 0 1+8x y? -)dx +( is an exact equation if A=

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Q: dy +y =2+2x dx

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Q: Solve the first order inhomogeneous equation dy + 2y = 3x2 dx Hint:

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Q: + Use Separation of variables to solve eくX<| Us co,t)こ0 I4 pts] ULx,0) = X

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Q: M(x,y) + N(x,y)*dy/dx = 0 ? is it Exact Equation?

A: Consider the equationMx,y+Nx,y×dydx=0provided that there exists a function ψ(x,y) such that∂ψ∂x=Mx,y…

Q: 4. Solve the equation using homogeneous equation (x– 2y)dx+(2x+ y)dy = 0.

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Q: B. Solve the following equation using the determination of integrating factors. 2. y(4x + y)dx –…

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Q: Use Picard's method of successive approximation to solve the equation 1+ xy, y(0) - 1 at x-0.1.

A: The solution of the differential equation is defined as the function that satisfies the equation.…

Q: (b) Use the substitution u = x In y to solve the equation (ry + 2ry In² y + y In y)dx + (2x² In y +…

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Q: Use Variation of Parameters to find a particular solution to the non-homogeneous equation y′′−2y′+y=…

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Q: dy Solve I +y= 1 given that y = 2 when t=0. dt

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Q: c). Using an integrating factor solve the equation dy , 4. +y= 3x dx

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Q: Solve for the solution for the equation: (x² + 3xy)dx + (x² + 4y) dy = 0 with the condition of y(2)…

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Q: So S (2x + 3z – y). dz. dy. dx B- Solve

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Q: Express æ = e-t, y = 2e2" in the form y = f(x) by eliminating the parameter y =

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Q: z = xy dy x + y = 2x/1-x²y² 2. Using the substitution change the "dx to a separable equation. Hence…

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Q: Solve for y(t) where y(t) + 2 / a – u)y[w)du = t.

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Q: dy х у ++1 y dx

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Q: (ztan 2 +1) dx – x dy = 0

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Q: Q1) Solve the following equation with Bernoulli equation Method, where x(0) =1 dx x* = 2x dy

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Q: determine the general equation; variable separable, homogeneous, exact, non-exact DE…

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Q: Find the solution of the this differantial equation. extan(y)dx + [(ex)/(x-1)]dy = 0

A: Hair we use the variable separable method to solve this equation.

Q: 3e2º sec 20 dy determine de Given y = V(0-2)

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Q: (b) Solve the following initial vahue problem by separation of variable = 2x at x = 0, y=-2 dx

A: We will solve the problem

Q: b) Find the general solution of (3sin y– 5x)dx+2x² cot ydy = 0

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Q: Find the 2nd solution using variation of parameter. y" + 16y=0; y₁ = cos4x For the toolbar, press…

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Q: Find ø(0) for a solution ø(x) to the IVP (sec x)dy= 2/y+1dx; Ø(t) =8.

A: GIVEN : (sec x) dy = 2 y + 1 dx                 ∅ (π) = 8

Q: Solve the equation (x^2-3y^2)dx + 2xydy = 0 using y=v.x and u transforms

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Q: Solve the Euler equation 2r dy 2.x dx? -3r given that y(1) =1 and y'(1) = 2. +3y 0 dx jntaios

A: To solve given differential equation first we write the auxiliary equation and find the roots and…

Q: Solve for the DE equation associated by the given function: у %3D Ае2* + Ве* + С. а.

A: the given solution of differential equation isy=Ae2x+Bex+C

Q: z = x+ y dy_ x + y +2 1. Using substitution change the dx x+ y+7 to a separable equation, Hence…

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Q: Solve the equations by variation of parameters. d2y/dx2 -dy/dx = ex cos x, x&gt; 0

A: d2ydx2-dydx=excosx

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.