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Solve the initial-value problem: (dx/dt)+(tant)x=(cost)^2, x(0)=-1.


Bernoulli's DE

(2y^3-x^3)dx+3x^2ydy=0
(2y^3-x^3)dx+3x^2ydy=0
(a) Find the integral surface of the following partial differential equation: (6) x(z+2a)p+ (xz+2yz + 2ay)q=z(z + a) Also find a particular solution passing through y = 0, 23+x(z + a)

Use Euler’s method with h = 0.25 to obtain a numerical solution of

dy/

dx= −xy2

subject to y(0) = 2, giving approximate values of y for 0 "\\leq" x "\\geq" 1. Work throughout

to three decimal places and determine the exact solution for comparison.


Solve the following difference equation "\\Delta\\lambda^k=-k+5; \\lambda^6=0"


(D-5D
(2y^3-x^3)dx+3x^2ydy=0

Discuss in detail all cases of the roots of a second order linear differential equation with constant

coefficients.


(D2 -2D +3)y = x2 -1


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