Math Answers

Prove that all real of the form  a + b 2, a; b ∈ Z forms a ring

Find aba-1 where (i) a = (5, 7, 9) , b = (1, 2, 3) (ii) a = (1, 2,5)(3, 4) , b = (1, 4, 5) .

If G is the abelian group of integers in the mapping T: G → G given by T(x ) = x then prove that as an automorphism

Let G be a group of order 112:132 . How many 11-sylow subgroups and 13 sylow subgroups are there in G?

Using Charpit’s method, solve:

P²+ q² -2px -2qy +1=0

Find the integral surface of the equation:

(x²-yz)p+(y²-zx)q =z²-xy

passing through the line x=1 , y=0

Find the integral curves of the differential equation:

(D³-D'³) z=x³y³

Using Charpit’s method, solve the equation:

zp²-y²p+y²q =0

Using Charpit’s method, solve the equation:

zp² -y²p +y²q =0

Using the method of undetermined coefficients, solve the equation:

d²y/dx² -3dy/dx +2y=4x²