The solution of the ODE * dy_ (x² + y²) || dx x2

Q: ® Find ('-x"]* d x [itx"]?

A: The given integral is:

Q: (xy^2+y)dx -xdy =0

A: Given: (xy2+y)dx-x dy=0

Q: x' -x? dxp x* +2x2 +1

A:

Q: det(A) Show that det(AB-') = %3D det(B)

A: Consider, Let A and B be the two n×n matrix, Now Consider, detAB-1 We know that the theorem, Let A…

Q: In x /1+ (In x)² -dp-

A:

Q: y=c_1e^x+c_2x^3

A: Elemination of arbitrary constants

Q: . How we Can Solne it ? 2. *B" (K+t) Carzz) (a+3) KB (ati) (a+2) %3D

A: Some formulae's: (a+b)2=a2+b2+2ab Power addition: (xayb)(xcyd)=xa+cyb+d

Q: (x^3 + x^4)dx + 8y^(3)xdy = 0

A: x3 + x4dx + 8y3xdy = 0

Q: On which interval(s) is the function h(t) = (−t^3) + 3(t^2) + 24t − 11 decreasing?

A:

Q: Calculate (3+1 x3+x a) using partial fractions b) using the substitution w = x3 +x

A: a) Given : ∫3x2+1x3+xdx  By Partial fraction  First, factor the denominator, we get 3x2+1xx2+1 =…

Q: Suppose f(x)=x^4+3x+1 on the interval [−4,−1]. Find x when f′(x)=0.

A: Given function is Differentiating with respect to x , we get

Q: (2x + 4) + 1 (2x +4) +1 dx: x2 + 4x + 5 x2 + 2x- 10 2 2 2 Consider dx = x2 (x2 + 4x + 5) dx evaluate…

A: We can solve as follows

Q: Find f such that f'(x) = 4x – 3, f(4) = 0. %3D %3D f(x) = D %3D

A: Given that: f'(x)=4x-3, f(4)=0

Q: 1−xy)^−2dx+[y^2+x^2(1−xy)^−2]dy=0;y(2)=1

A:

Q: (1) Let A={1,{2},{1,{2}}} (a)True or false: 2 € A, {2} € A, {{2}}CA, {1,2}CA, 3x(x € A^xA)

A:

Q: P(A)=0.3, P(B)=0.6, A and B are indep, find P(AB'), P(A|B')

A: We have given that  P(A) = 0.3 P(B) = 0.6 If A and B are independent then, P(AB) = P(A and B) =…

Q: Determine n=0 1 L th (2n + 1)! An (x) An+1(x) dx, from the relation: n tn+1 LA -1 An (x) An+1(x) dx

A: Given Information:To find:The value of .Concept used:The power series of sine function is .

Q: | A = S² - (x - 1)³ dx + S³² (x-1)³ dx

A: We have to solve the given definite integral.

Q: Eliminate the arbitrary constants of y=ce*+₂4-sin3x

A:

Q: If f(x) = (4x – 2)² - (3x² + 6)", find f'(4).

A:

Q: find x in f(x) = 45 − 0.42x + 0.006x^2

A: The given equation is,