Verify that y(x) = A+Be^-x is a solution to the initial value %3D problem y'(x) +y(x) =0 with u(0)=2. Find A and B. Solve the ordinary differential equation (ODE) 4 d/dx y(x)+ 2y(x) =6x+6 with y(0)=1. QUESTION 36!

Q: consider the differential equation x^2 y''-x(x-2)y'+(x+2)y=0 , y1=x is a solution find y2

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Q: Find the general solution of the differential equation 14y^(4)+57y''+25y=0

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Q: Solve the differential equation. (y^2)*(y") = y' Please show work!

A: The given differential equation is: y2y''=y'. We have to solve the given differential equation.

Q: Find the solution of the differential equation that satisfies the given initial condition. (Write…

A: The given differential equation is; 5xcos(x) =[2y+e^(3y)]y', y(0)=0.

Q: Solve the following differential equation by finding yp by inspection: (D^5+4D^3)=7 * O y = C1 + C2x…

A: We will find out the required solution.

Q: find the general solution of the differential equation y'+yx^5=(x^5)(y^7)

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Q: One solution of the differential equation y''+y'=0 is y=e^-x. A second linearly independent solution…

A: We will find out the required solution.

Q: The differential equation formed by eliminating a and b from y = ae* + be* is

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Q: Find general solutions of the differential equation    (x^2-1)y'+(x-1)y=1

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Q: Show the solution that y=(1+Ce^(x^6))^(-1/6) is the general solution of the differential equation…

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Q: To make the differential equation 2ydx + xdy - x^3dx = 0 exact, what must be the integrating…

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Q: find general solutions of the differential equation y^(3) * y' = (y^(4) + 1) cosx

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Q: y" + 4xy' +(4x² + 2)y=8e¯x(x+²); _y₁ = è¯ e

A: This is a problem of differential equation.

Q: Find the general solution to the differential equation y' + xy = x/y2 Are there any solutions for…

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Q: 1.Solve the Differential Equation (D^2+3D+2)y=4t^2 using a. reduction of order, and b. variation of…

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Q: (D² -1)y= 2(1-e-2*)-1/2

A: By Using  variation of parameter

Q: Give the detailed solution of this differential equation using 1st order and 2nd order 1. (y') ² +…

A: This is a problem of differential equation.

Q: The math problem is (3xy^2-2y^3+3)dx = (-x^3+6xy^2-2y)dy  I believe this is a Exact Differential…

A: We have to show that given differential equation is either exact or not.

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.