Question (01): Solve the following homogenous differential equations. +y+Jx=y) dx -«/x+y--y) dy = 0 i.

Q: 3) yy +x²(sinx)³ = y³cotx %3D

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Q: Prove that the differential equation is not exact ey (e" + ") - s/ = 0 2+ + -

A: Exact diffretaial equation

Q: Determine the form of a particular solution for the differential equation. Do not solve. y" +22y' +…

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Q: Consider the function f(z) which maps the upper-half plane into the quadrilateral with vertices at ±…

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Q: (2xy-tany) dx + (x^2 - xsec^2y) dy = 0

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Q: Find the solution of the differential equation (1+x* )y'+2.xy – 4x°y° = 0 (Bernoulli) %3D

A: We will find out the required general solution .

Q: Solve the following differential equations: (DE in 1st Order, 2nd Degree) 10.) 2(y')?tan?x - y'tan³x…

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Q: (2x + 3)y' = y +(2x + 3)/2; when x = –1, y = 0 %3D %3D

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Q: (t + 2)°y" + 3(t + 2)y' +y= 0, 1>-2, V1 = (t+ 2)

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Q: 5) Find all the singular points for the given differential equation. Classify each one as regular or…

A: Step:-1 Let P(x)d2ydx2 + Q(x) dydx + R(x) y =0 -----(1), be the differential equation of second…

Q: y" - 6y' + 8y = 0

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Q: Solve Cauchy Euler differential equation x²y" - 7xy' + 41y = 0

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Q: Solve the ordinary differential equation 3xy" + (2 - x)y' - 2y = 0. Then evaluate the first four…

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Q: SHOW COMPLETE SOLUTION PLS. Show that y=ex(1+x) is a solution of the differential equation…

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Q: Folve differential equation by variation of parameters. y" – 4y' + 4y = 2e2

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Q: 2.) (x +2y-1) dx - (2x +y - 5) dy = 0

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Q: Given the differential equation dy _ (4x + y)(x + y) dx x > 0. x² a) Find the general solution of…

A: The given differential equation is                           dydx= 4x+yx+yx2,   x>0 we solve the…

Q: Find the Differential Equation whose general solution is y = C₁e4t + C₂e-3t Oy" - y' +12y = 0 y"+y'…

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Q: ' + y' - 6y = 3x - e2r y' е

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Q: Solve the differential equation xy' - 3y = 2x° In x. The solution is y = (Type an expression.)

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Q: For which value of the constant c is the function y = 15e-® + x + c a solution of the differential…

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Q: y'+9xe"+3* = 0 y+3x

A: We use method of Variable separable to solve this differential equation

Q: SOLVE FOR the differential equations 15) (2x - 5y + 12) dx + (7x - 4y +15) dy = 0

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Q: The indicial equation for the differential equation " +7y-5xy 0 is O A. (r+ 7) = 0 O B. P(7r - 1) =…

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Q: find the solution of differential equation 2 y3 y' +- y

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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.