Solve the following differential equations using classical methods and the given initial conditions: d²x (a) +6df + 8x = 5 sin 3t, dt² d²x (b) ² + 4x=t², x(0) = 1; dt2 x(0) = 0; x'(0) = 0 x′(0) = 2

Q: (b) Use the substitution x = e' to transform the Cauchy-Euler equation x²y" – 4xy' + 6y = 3x² +…

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Q: [4x³cos(xy)-x^ysin(xy)-yex+3x²]dx -[x³sin(xy)+ xex+6y²]dy=0

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Q: Solve the differential equation: [y³ – y²e* – cos(x – y)]dx + [3xy² – 2ye* + cos(x – y)]dy = 0 ;…

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Q: dy +ky = a sin bx dx %3D Show that the solution of the differential equation is given by: 2 +b²+ab K…

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Q: Solve the following first order differential equations.  yy' = (y2 - 1)(x2 + 1)

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: Find the solution r(t) of the differential equation with the given initial condition: r' (t) = (sin…

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Q: (b) Consider the differential equation ydx + x(lnx-lny - 1)dy = 0. (i) Show that the equation is a…

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Q: Q3/ A: Find General Solutions for the following Differential Equations (Use Differential Operators).…

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' + 50y = ex cos(7x) y(x)…

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Q: ln y to solve the differential equation (xy + 2xy ln² y + y ln y)dx + (2x² In y + x)dy = 0. (b) Use…

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Q: x In x = y(1 + 3 + y² ) y', y(1) = 1 %3D

A: Let us consider the differential equation of the form dydx=f(x)g(y) Then to solve the equation using…

Q: the given differential equation is not exact and hence show that Solve it x²ydx -lx3+y?)dy=0

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Q: Solve the following differential equations (a) y/ = (b) = %3D ytev

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Q: Solve the given differential equation by undetermined coefficients. y"+2y=-18x²2x

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Q: (a) Solve the Cauchy-Euler equation solution of the differential equation r²y" + xy + 4y = 0, r> 0.…

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Q: Solve the given differential equation by separation of variables. csc(y) dx + sec²(x) dy = 0 s(x):…

A: To solve the given differential equation using separation of variables

Q: 7) ( x² + 6y? ) dx - 4xy dy = 0 y(1) = 1

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Q: Solve the differential equation with its given initial values Uxt = 3x² In(x + 2) WITH u(x,0) =…

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Q: Determine the type of Differential Equation, then find the solution for it.

A: The type of equation is bernoulli equation. In fact we have converted it later by assuming z=y'  we…

Q: Consider the differential equation [ (1-by sin(x)) + 2 cos(x)y' = 0.

A: Given the differential equation is                         (1-bysin(x))+2cos(x)y'=0.

Q: dy (e2y – y)cos(x)- e' sin(2x), dx y(0) = 0

A: on solving this we get the

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

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Q: Solve the given differential equation by undetermined coefficients. y" + 2y'=2x+9-e-2x

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