5. Verify that the indicated pair of functions is a solution of the given differential equation on the interval (-00, 00). dx = x + 3y dt dy = 5x + 3y dt -2t X = e + 3e6t -2t y= -e + 5e6t

Q: 4. Verify for r > 0, that y = a/2 is a solution of the nonlinear differential equation yyll = x.

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Q: (3) Show that the solution of the differential equation fip + y = -2r"y' is ´d.r r'y"(2r* + c) = 1.

A:

Q: 2. Show that k(x, y) = e2ª cos (x + In y) is a solution to the differential equation 2k – ykya = 5k.

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Q: Find the general solution of the second order differential equation below: dx d) dt2 + 6x = 0 dt

A:

Q: 2. Verify that the function y = Cjex + C2e2x is a solution of the differential equation y"– 3y' + 2y…

A: Given, the function y=C1ex+C2e2x is a solution of the differential equation…

Q: determine the general solution of the given differential equation.  y(4) − 4y″ = t2 + et

A:

Q: The solution of the differential equation dy dx 2x+12 is 2y-9 O y? – x? = C - O y – 9y – x² – 12x =…

A: Solve by variable separable form

Q: Investigate the solution of the second order differential equation d²v + (4 × 10-6)v = 0 dt2 dv with…

A:

Q: Verify that the indicated function is an implicit solution of the given differential equation.…

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Q: Find a particular solution of the following nonhomogeneous differential equation in t using…

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Q: Verify that the function y = e-3x is a solution to the differential equation d2ydx2 + dydx − 6y = 0.

A: We have to verify the solution

Q: 5. Find the solution of the differential equation that satisfies the given initial condition. dy =y²…

A: Topic- differential equations

Q: 2.2 Find the solution of the differential equation d'x dx + + 3z + 8x dt dz %3D dt? dt

A: Given: d2xdt2+dxdt+8x=dzdt+3z

Q: Find the solution of the differential equation that satisfiesthe given initial condition.

A: The given differential equation is dLdt=kL2lnt  Initial condition L1=-1.

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

A: Given first differential equation(y-x)y'=y-x+2To find: y=x+2x+6 is the solution of the given…

Q: | 2. Consider the differential equation y(5) + 3xy4) + 2y = 0 How many linearly independent…

A: **By Bartleby policy I have to solve only first one as these are all unrelated problems**  First…

Q: (6) Show that the solution of the differential equation dr 3 + dy 3(y + 1) is r (y + 1)³ + c y +1 y…

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Q: Find the solution of the differential equation that satisfies the given initial condition. x In(x) =…

A:

Q: By using the substitution z = y², convert the differential equation dy x²y- xy2 = 1. dx to a linear…

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Q: Find the solution of the differential equation (In(y))³ dy dx = x'y 3 which satisfies the initial…

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Q: The solution of the differential equation + 25y 0 is dy Oy= Acos25x + Bsin25 O y (Ar + B)e 5 O y=…

A:

Q: Find the general solution of the first-order linear differential equation (dy/dx)+(1/x)y = 6x + 2…

A: Given- dydx+1xy=6x+2 To find- the general solution of the above first order differential equation.…

Q: Match the differential equation with it's particular solution form. | y’’ – 6y' + 9y а. Ate 2t |y'’…

A: We have to match the following differential equation with it's particular solution form.

Q: determine the value of C of the general solution of the separable differential equation dy/dx= xy^2…

A: From the given problem: dydx=xy2 So, dydx=xy2dy=xy2dxdyy2=xdx Now integrate on both side:…

Q: Find the particular solution of the given differential equations. (x² + 2xy - 4y²)dx - (x² - 8xy -…

A: Given equation is (x2+2xy-4y2)dx-(x2-8xy-4y2)dy=0

Q: 2. Make up a differential equation of the form dy dt that has the function y(t) = e²t = 2yt+g(y) as…

A:

Q: 3. The particular solution of the differential equation dy for which y(0) = 20 is dt 4 O y =…

A:

Q: Verify that yp(x)=2e6x is a particular solution to the differential equation y′′ − 2y′ − 15y =18e6x…

A: Given, y''-2y-15y=18e6x Particular solution: ypx=2e6x

Q: 3. 3(x² + y²)dx + x(x² + 3y2 + 6y) dy = 0; when x=2, y=0

A: follow next step

Q: 4. Show that the coefficients of the given differential equation are homogeneous and solve the given…

A:

Q: Find the particular solution of the given differential equations. 2. (x² + 2xy - 4y²)dx - (x² - 8xy…

A: (x² + 2xy - 4y²)dx - (x² - 8xy - 4y²)dy = 0

Q: Find the particular solution of the differential equation dy (х — 5)е 2у -2y dx satisfying the…

A: To find the particular solution of given differential equation.

Q: 4. Use separation of variables to find the general solution of the differential equation. dy = 5t+1…

A:

Q: Find the particular solution of the following second order differential equation d² y dy dx² --4-…

A: The given differential equation is :d2ydx2-4dydx-21y=-105x-209given that y0=11 ; y'0=39.

Q: Find the solution of the differential equation that satisfies the given initial condition. dy = (8x…

A:

Q: Write down the form of the general solution y = y. + y, of the given differential equation in the…

A: Consider y=emx be the solution of the homogeneous part. The auxiliary equation is m2+w2=0. Simplify…

Q: The differential equation –y" = f(t), y(2) = 0. y(5) = 0 discretized with step-size h = has the…

A: The given equation is  -y''=f(t) Then the function f(t)=2t+1 We solve this equation by Euler's…

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

A:

Q: Determine the interval for which the solution of the differential equation  y(iv) + 4y''' + 3y = t-1…

A:

Q: Find the general solution of the Euler-Cauchy differential equation (x'D² – 4xD+6)y = 0

A:

Q: 5. Verify that the indicated pair of functions is a solution of the given differential equation on…

A: We need to verify that given pair of function is a solution of the given system of differential…

Q: . Find the explicit general solution to the given differential equation. Hint: Linear DE. (2x + 1)y'…

A:

Q: Show that xand x-³are solutions to the higher order differential equation x?y" + xy' – 9y = 0 with…

A:

Q: 6.Solve the linear differential equation for general solution

A: Let, The characteristic equation of the given differential equation is,…

Q: 3. Verify by direct substation that y = > Cn x", is a solution of this linear differential equation…

A:

Q: | Find the solution of the differential equation (In(y))³ dy = x'y dx which satisfies the initial…

A:

Q: 14. Solve the differential equation dy t dt y y(0)=1 by the Euler method with h=0.1 to get y(0.2).…

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Q: –7 + 12 d5x 7) 25 d*x -7- dt5 d²x + 12 dt3 + 8. = 0 dt4 dt2

A:

Q: 2. Verify that the indicated expression is a solution for the given differential Equation dy x3y3 –…

A:

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.