(1) Verify that the indicated function is a solution of given DE: (i) y" – 4y' + 4y = 0; y = c1e²x + c2xe²x (ii) y"+y = tan x; y = -(cos x) In(sec x + tan x)

Q: initial conditions. f ''(x) = 6 cos(x), f '(0) = 5, f(0) = −9

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Q: Verify that the function y = 6x − 4 sin x + 1 is a particular solution of the differential equation…

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Q: y = (C₁ + C₂x) eª + sinx+x²; y" - 2y' + y = −2 cos x + x² − 4x + 2

A: Here we find the first and second derivatives of given solution and then put in the left hand side…

Q: 15. What is the general solution of the exact differential equation (x + siny – cosy)dx + x(siny +…

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Q: Determine which functions are solutions of the linear differential equation.y″ + y = 0 (a) ex (b)…

A: Given linear differential equation is (a) Therefore, y=e^x is not solution of given differential…

Q: Show that y = sin−1 x satisfies the differential equation y = sec ywith initial condition y(0) = 0.

A: The given differential equation is y' =  sec y,  with initial conditions y(0) = 0.We want to show…

Q: 5. Find the general solution for the differential equation -(sin y + y sinx )dx + (cos x – x cos…

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Q: Verify that the function y = x sin(x) + x cos(x) is a solution to the differential equation: y" + y…

A: 1 have verified the differential equation by finding each derivatives

Q: Obtain the solution to the differential equation: cos*x- cos"y dx + cosxsin 2ydy = 0 a. cos*y(1+…

A:

Q: Determine whether the function y = x2 ex + sin x + cos x is a solution of the differential equation…

A: Here given function as y = x2 ex + sin x + cos x .....(1)

Q: Q4// Solve the partial differential equation a²u ди cos*x given that = x when y=0 and u=3 when x=0?…

A: The given partial differential equation is ∂2u∂x∂y=cos4x Integrating on both sides with respect to y…

Q: Verify that y=sinx is a solution to dx dy 2cos x-sin x+y and solve the 2 cosx differential equation…

A: Given Information :  Differential equation : dydx = 2cos2x - sin2x + y22 cosx  y1 = sinx y(0) = -1

Q: The solution of the differential equation is dy Y =sin x dx x O x(y +cos x ) = sin x +c O x(y - sin…

A:

Q: Evaluate the general Solution to the differential equation: Cy-cos-x)dx+ cosxody A y(secx + tan x) t…

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Q: To solve the ordinary differential equation dy +xx dx = sin x, y(0)= 5. 3 by Runge-Kutta 4th order…

A: The form of differential equation to use Runge kutta 4th order method

Q: What is the general solution to the differential equation sin y (x + sin y)dx + 2x² cos y dy = 0 ?…

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Q: Solve for the differential equations of  (e^x sin y - 2y sinx) + (e^x cosy + 2 cosx)y′ = 0

A: Given : (e^x sin y - 2y sinx) + (e^x cosy + 2 cosx)y′ = 0

Q: 29. Verify that the piecewise-defined function 1-x², x<0 x ≥ 0 is a solution of the differential…

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Q: 1. Find the general solution of the linear differential equation using undetermined coefficients,…

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Q: Give the general solution of the differential equation p"+ 25 y =2 sec( 5 x) a) O y=C, sin(5 x) + C,…

A: To find  The general solution of the given differential equation.

Q: sin x sin y dx + cos x cos y dy = 0 %3D

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Q: 9. Solve the differential equation (2 sin?y + 4x² sin y)dx + (3x sin y cos y + 2x³ cos y) dy = 0…

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Q: y' + (2 tan x)y = - cos'x

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Q: Show that the solution of the differential equation dy/dx=sin(x+y)+cos(x+y) is  1+tan(x+y)/ 2 =…

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Q: What is the general solution to the differential equation sin y (x + sin y)dx + 2x² cos y dy = 0 ?…

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Q: If the function y = A sin z + B cos a satisfies the differential equation y" + y – 2y = sin z for…

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Q: Determine the solution of the differential equation y" + y = sec² а. y = C, cos x + C2 sin x – cos x…

A: The given differential equation is; y" +y'=sec2x

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

A: The solution is given as

Q: Find the particular solution of (cos x – x sin x + y²) dx + 2xy dy = 0 that satisfies the initial…

A: Make the absolute form and solve this differential equation.

Q: 2. Solve the differential equation using undetermined coefficients satisfying the given conditions.…

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Q: Show that an implicit solution of 2x sin?(y) dx – (x² + 17) cos(y) dy = 0 is given by In(x2 + 17) +…

A: To find- Show that an implicit solution of 2x sin2y dx - x2 + 17 cosy dy = 0 is given by lnx2 + 17 +…

Q: Solve the exact differential equation (In y - y sin x-6e)dx+(÷- + cos x + 5 sec y tan y -6y)dy = 0 A…

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Q: 2(a) Given that f(x, y) = 6x²y3 – cosx + 5y – siny + 10x, establish the fact that, the order in…

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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: Find the solution of the differential equation y" + y' = sin x -sinx +cosx а. y = C1 + C2 e¬x SX b.…

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Q: Verify by substitution that the family of functions y = -(x) sin(-3x) + cx is a solution of the…

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Q: Obtain the solution to the differential equation: y cos x(2y sin x+ 1)dx+ (sin x- 2y cos²x)dy = 0-…

A: The given differential equation is: y cos(x)2y sin x+1 dx+sin x-2y cos2x dy=0

Q: Use Euler method to estimate the solution of 1 sin 5x - 5e cos 5.x, dx with initial condition v(0)=0…

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Q: Find the function y: (0.x) → R that satisfies the ordinary differential equation ry'(x) + y(x) = x²…

A: Given : y : 0 , ∞→ℝ   ;  xy'(x)+y(x)=x2 cosx        ;  yπ = 0 To Find : solution of ordinary…

Q: A solution to the partial differential equation. u u is None cos (3x – y) 2² + y? -3 sin (7x) sin…

A:

Q: Express the solution of the given initial-value problem in terms of an integral-defined function.…

A: The given differential equation is dydx-4xy=sinx2,y0=7.

Q: Verify that the indicated function y = y(x) is an explicit solution of the given first-order…

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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: To solve the ordinary differential equation dy 3+5y' sin x, y(0)= 5 dx %3D by Euler's method, you…

A: we have,3dydx+5y2=sinx, y(0)=5

Q: Obtain the solution to the differential equation: (cos'x- cos'y ]dx+ cosx sin 2ydy = 0 a. cos"y(1+…

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Q: SOLVE FOR THE PARTICULAR SOLUTION OF EVERY DIFFERENTIAL EQUATION GIVEN. 1. x In x sec? y dy + [tan y…

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Q: 3. Let the function y = y(x) satisfy the equation (y – x)² = 1 + 3(y +æ)*. Show by implicit…

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Q: Find the particular solution of the differential equation (2xy - sin x)dx + (x² - cos y)dy = 0, when…

A: Exact differential equations

Q: What is the general solution to the differential equation (tan x)dy – (4yIn y – y tan³x)sec?x dx = 0…

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Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: We will convert given differential equation into linear differential equation by appropriate…

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.