If y = f(x) is the solution of æy' + 13y – axy? = 0, f(1) = 12/a, where a + 0 is a re а, number, then

Q: y', In(y) 1 y(e) = 1. x² In(x)

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Q: Solve the initial value problem y' + 2y At), y(0) = 0 %3D

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Q: Find the general solutions of the differential equations in Prob- lems 11. y(*) – 8y(5) + 16y" = 0…

A: SINCE YOU HAVE ASKED MULTI PAL QUESTIONS IN SINGLE REQUEST , WE WILL BE ANSWERING ONLY THE FIRST…

Q: Let y be the solution of the initial value problem y′′+y=−sin(2x), y(0)=0, y′(0)=0. Find the maximum…

A: Here, differential equation is y’’+y=-sin2x

Q: Which term is included in the solution of the differential equat y" – 2y' – 3y = e y(0) = 1, y'(0)…

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Q: yy' – xcos(x²) = 0, y(0) = -2

A: We have to find the particular solution of the given initial value problem.

Q: Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the…

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Q: Solve the IVP u® +u"=e*-2tx with y(0)=1, y'(0)=0, y"(0)=1 (where t is a real constant)

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Q: Find a particular solution to y" + 5y' + 6y = lte".

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Q: x²y" +xy' – y = T

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Q: Use Euler's method with step size 0.3 to estimate y(1.5), where y(x) is the solution of the…

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Q: Solve the initial value problem given by y' = (x2 + 2y2)/(xy) ,  y(1) = 1 What is the interval of…

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Q: Verify that y=2 cos(3x) is a solution to the initial value problem: y"+9y=0, y(0)= 2

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Q: 3. Show that the equation (6xy – y*)dr + (4y + 32² – 3ry²)dy = 0 %3D is exact. Hence solve the…

A: Given that  The differential equation is  To solve the differential equation with intial condition

Q: Use Euler's method with step size 0.4 to estimate y(0.8), where y(x) is the solution of the…

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Q: Let y be the solution of the initial value problem y" + y = – sin(2x), y (0) = 0, y' (0) = 0. The…

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Q: 5. Obtain the particular solution. y'"-2 y'+2 y=3e" cos 2x; when x 0, y=2,y'=3

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Q: Use Variation of parameters to find the solution of the initial valuue problem 3y = t², y(1)

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Q: Find the largest interval in which the solution of the initial value problem y" + csc(t) y' +…

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Q: 2xyy'=1+y; whent = 2, y = 3 Ans. y = 5x-1

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Q: 4. Verify that the solution of the DE d²x dt² + k²x = 0 is x = sin(kt).

A: To verify that the solution of the DE d2xdt2+k2x=0 is x=sinkt.

Q: The solution of y" – 2y' + y = 0 with initial conditions y(0) = 1 and y'(0) = 0 is given by?

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Q: 91, Sove a, ychea (2ay-e3) dy- 0 b, Solve initial value problem (37'+ 9ay Sy')de - (bx'4liny) dy- 0…

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Q: What are the equilibrium solutions of the DE dy /dt=−3(2−y)?

A: given DE  is dydt=-3(2-y)

Q: Use separation of variables to solve the initial value problem. dy 2xcos² y; y(3) = 0 dx

A: Here we have to solve the givne differential equation.  dydx=2xcos2y; y(3)=0

Q: Use Euler's method with step size 0.2 to estimate y(0.4), where y(x) is the solution of the…

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Q: Use Euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the…

A: Converting the given equation into Euler iteration:…

Q: Find the general solution of the Cauchy-Euler equation: x²y" – 3xy + y = x°, x>0.

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Q: 6. Show that y(x) = Inx is a solution of xy" +y' = 0 on interval (0, 00) but is not a solution on…

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Q: Use Euler's method with step size h = 0.5 to approximate the solution to the initial value problem v…

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Q: Express the solution of the initial value problem dy 2x- dx as an integral = y + 2x cos x, y(1)= 0

A: Simplify and convert in linear equation.

Q: 3- Find non-zedo solution ofs dy

A: we need to solve the given first order nonlinear differential equation. The given equation is…

Q: Find the Wronskian of two solutions of the differential equation t²y" – t(t – 4)y' + (t – 2)y = 0…

A: The given differential equation is t2y''-tt-4y'+(t-2)y=0. We need to find the Wronskian of two…

Q: Solve the initial value problem u(t) du dt 4u-+-3t u(0) = 9

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Q: Verify that u(r, t) = f(e-"x) solves the initial value problem (au + z8,u = 0, u(x,0) = f(z).

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Q: Verify that u(z, t) = f(e'r) solves the initial value problem (a,u + z8,u = 0, u(x,0) = f(x).

A: Take the partial derivatives of u(x,t).

Q: Solve the initial value problem - zy, y(0)-0.35502805. (0) 0.25881940 --

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Q: 9. Find the solution to satisfying y = dy dt = 7y || y(6)=9

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Q: Let A = |. Solve the initial value problem y'(t) = Ay(t), y(0) = 2:

A: Given matrix A=2−112 For a system of differential equations y't=Ayt, assume solution are taking the…

Q: Verify that the function y(r) = 2, is a solution of the initial value problem dy + 2y = 3y, v(0) =;…

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Q: Determine the longest interval in which the initial value problem (8t + 6)y" + 3ty – 4y = 3 cos(t),…

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Q: The differential equation of the form M (x, y) dx + N (x, y) dy = 0 that has been transformed to M1…

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Q: A- solve = x + y² with condition y (0) = 1, x o= 0 to x =0.2 and h = 0. by Rung kutta dx method 4th

A: The given differential equation is dydx=x+y2 with conditions y0=1, x0=0 to x=0.2 and h=0.1.

Q: Solve the first order Initial Value Problem by using Runge Kutta method of order 2 and 4. xy' = y…

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Q: Use Euler's method with step size 0.1 to estimate y(0.5), where y(x) is the solution of the…

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Q: Find the solution of the initial value problem ty' +2y-2 sint, y(x/2)=1,

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Q: 7. Use the Fourth Order Runge-Kutta method to solve y'-y = 0, y(0) = 1 on the interval 0, - v with h…

A: The formula for the fourth order Runge-Kutta method is dydx=f(x,y) with the initial condition x0, y0…

Q: Find the solution of the given initial value problem in explicit form. ㅠ sin (2x) dx + cos(7y) dy =…

A: Here we use basic integral to find the solution.

Q: Verify for r > 0, that y = /2 is a solution of the nonlinear differential equation yyll = r.

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Q: Find the particular solution of xy' - 4y = 0 ; initial condition y = 2 when x = 1.

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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.