Allow y(x) be the solution for the following initial value problem and then find y(e):  dy/dx = (lnx)^6/x*y^2 ,  y(1)= 3

Q: If ( 1 + x²)(1 + y²) - px² = 0, where p is a constant, show that xy ( 1 + x²)dy/dx = ( 1 + y²).

A: Given: To Find:

Q: 3 3. y' for y² = x²y³

A: to find out the derivative

Q: 1 I = J dx (1-x²)Z %3D 3

A: It is known that: 1-cos2x=sin2x∫sec2x=tan x+Ctansin-1x=x1-x212

Q: 4. Solve dx -dy = 0 %3D x²y xy?

A:

Q: Solve of the following Clairaut equation y=((x+4)y')+(y')^2

A:

Q: i) Find the derivative of g(x)= 4x2 ii) If y³+2y-4x=5 find dy/dx cosx

A: Given: (i) g(x)=cos(x)4x2(ii) y3+2y-4x=5

Q: 4x – 9y = 1 find the first derivative

A:

Q: What is exact solution for dy/dx =(x2+y2)/(x+y)

A: Given: The given equation is dydx=(x2+y2)x+y

Q: If y = (x+1)/(2x - root x' then y' will be?

A:

Q: Solve dy/dx =(4x+y+1)2,If y(0)=1

A: dydx=4x+y+12 Now let, 4x+y+1=t Differentiating with respect to x, we get 41+dydx+0=dtdx⇒dydx=dtdx-4…

Q: Find the equation of the function f whoseg 3 f'(x) = (0, 4) %3D -- 1 + e

A:

Q: if y=(x+1/x)/(2x-3) the dy/dx will be

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.