Solve the initial-value problem y" + y = e-4 sin t, y(0) = 0, %3D y'(0) = 0. %3D

Q: y = Arctan ( 2+x 1-2x

A: We have to find derivative

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Q: Find the solution of the equation y^' = (1+y) sec ⁡x + tan⁡ x. and, Solve the equation x dy - y dx…

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Q: Solve for the first-order DE: y’+y-y^2(cos2x-sin2x)=0

A: Solution: A first-order Bernoulli ODE has the form of y' + p(x)y =q(x)yn Rewrite the form of…

Q: sec?xsec'y dx dy .2

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Q: Q1) Solve the differential euqation  dy/dx = xe^(-y) where y(1) = ln(1/2)

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Q: y'-(2/x)y=(y^3)/(x^2) find the solution that satisfies y(1)=1

A: The given differential equation is

Q: Solve following DE x^(2)y"-7xy'+16y=0

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Q: Use Variation of parameters to solve following y"-3y'+2y=e^(-x)

A: We know that Method of variation of parameters :If given differential equation is of the form  y″ +…

Q: Longest interval for (t+2)y’’-(sint)y’+ty/t-4=e^2t/t y(-1)=0

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Q: Y''+4y=cosx find solution

A: We have to find the solution of the differential equation y''+4y=cosx. Consider the homogeneous part…

Q: Solve y" -8y' +16y = 0

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Q: Solve the bernoulli equation dx/dy+(2/x)y=-x^2y^2cos(x)

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Q: Solve xy' = y +1

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Q: Solve the first order o.d.e dy/dx=(1+y^2)e^x

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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: Bernoulli's Equation Solve (dy/dx) - (y/x) = y2e^(x2

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: cos x )y+y'= e^(-sinx) solve the dif eq for the problem above  thanks

A: Given that  (cos x )y+y'= e^(-sinx)

Q: Find for implicit equation dx xy -e' = 3x*

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Q: Solve: y" + y'tanx = (y')²

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Q: (xy^2 - x^3) + (yx^2 - y) y' = 0, y(0) = 1, solve for y when x = 2

A: Exact differential equation problems

Q: y = tan e³x + etan3x

A: (tan x)' = sec2(x) (eax)' = a eax.

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.