Number Theory Exercise 1 Prove that the equation 3x^2 + 2 = y^2 has no solution...

Number Theory

Exercise 1 Prove that the equation 3x^2 + 2 = y^2 has no solution (x, y) ∈ Z × Z. (Hint: consider the associated congruence modulo 3.)

Exercise 2 Prove that the equation 7x^3 + 2 = y^3 has no solution (x, y) ∈ Z × Z. (Hint: consider the associated congruence modulo 7.)

Expert Solution

Colby Messinger answered 1 year ago

Find the general solution for differential equation x^3y'''-(3x^2)y''+6xy'-6y=0, y(1)=2, y'(1)=1, y''(1)=-4

a) Let y be the solution of the equation y ′ = sqrt(1 − y^2) satisfying...

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dervive the Frobenius solution to 4(x^2)*y"(x)+(3x+1)y(x)=0

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y'' + y=tanx+3x-1 solve the ode and find the general solution?

A discrete system is described by the difference equation y(n)= 2.5y(n-1)-y(n-2)+3x(n)+3x(n-2) a. Using Z-transform, Determine all...

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1.) Let f′(x) = 3x^2 − 8x. Find a particular solution that satisfies the differential equation...

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Sketch the region in the first quadrant enclosed by y=2/x , y=3x, and y=1/3x. Decide whether...

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1)Find the power series solution for the equation y'' − y = x 2)Find the power...

1)Find the power series solution for the equation y'' − y = x 2)Find the power series solution for the equation y'' + (sinx)y = x; y(0) = 0; y'(0) = 1 Provide the recurrence relation for the coefficients and derive at least 3 non-zero terms of the solution.

y'=√2x+y+1 general solution of differential equation

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