1. Show that if you differentiate both sides of x2 + 2y³ = 6, the result is 2x + 6y2 = 0. Then solve for dy/dx and evaluate it at the point (2, 1).

Q: 1-7ӕ + 3 | dx 4.

A: To evaluate the integral: ∫1-7x+x3xdx. Solution: Evaluating the integral.…

Q: 5. (1+2xVx2 - y² )dx-(2yVx2-y? )dy =0

A:

Q: 1. Find 2(3z + 4)² dz.

A:

Q: solve using non-exact (x+4y3)dy - ydx = 0

A: Solving the non exact differential equation

Q: Solve, (2x+3y-2)dx+(3x-4y+1)dy = 0 %3D

A:

Q: Solve for DE (x + 2y - 3)dx - (2x + 4y - 9) dy = 0

A: In this question,  we solve given DE by substitution methode i. e.  We put some terms in the form of…

Q: Solve (5x + 9y) dx + (9x+ 5y) dy

A:

Q: Solve 2- (2xy - 2y)dx + (3x'y-4x)dy 0

A: We have to solve given problem:

Q: 1. Solve: 2 dy (2y + 3) dx 4x + 5,

A: The answer of the differential equation is, 2/(2y+3) = 1/(4x+5) + c, where c is an arbitrary…

Q: dy dx 2xy + 6x + (x²-4)-

A: Solution of given question is written in below steps.

Q: L Lyx² exydxdy -y

A: We need to evaluate ∫-10∫-y1x2 exy dx dy The region of integration is given as Here -y≤x≤1-1≤y≤0 On…

Q: Solve (3x*y? – x²)dy + (4x³y3 - 2xy)dx 0 %3D | | .3

A: Given differential equation is exact differential equation. We solve it as follows:

Q: Solve for y. x= (3y+5)/(7y-1)

A: To solve for .

Q: Solve (2xy-2xy- = 0 4xy² +2x) dx + (3x2y + 4y) dy %3D

A:

Q: x²dx 3 2 3 (5-x') 2.

A:

Q: Determine an expression for expression for 3(y-2)³ − x² = 4x − 6. dx

A: Solving the problem by finding the value of the problem by finding the value of the derivative.

Q: dx 3x + y dy r+3y

A:

Q: Solve (xy+x)dx - (x2y2+x2+y2+1)dy=0 using separation of variable

A: Let's find.

Q: Find d2y/dx2. y=5x3/3   -2x

A: