Differential Equations Answers

If w = sin(x+kt) + cos(2x+2kt).
Prove that ∂^2 w/∂t^2 = (k^2).∂^2 w/∂x^2

solve the second order differential equation

y" - 3y' + 2y = 3e^(-x) - 10cos3x y(0) = 1 y'(0) =2

Find the solution of the equation div(grad z)(x,y)=(e^(-x))cosy which tends to zero as x tends to infinity.

Please solve the following:
1. y''=1+(y')^2
2. xdy-(3y+x^5*y^1/3)dx=0

Let u=2sin(x) and v=−4x−8.

Find the derivative of their product with respect to x.

ddx(uv)=??

power of x is 4+x square +1 -------differentiate it w.r.t x

Differentiate with respect to x:f(x)=(x+X^5)

1−5x^2
1+5x^4
5x^4−1
x−5x^4

Differentiate with respect to x:f(x)=(8x^3+X^2)

8x^3−x
24x^2−2x
2x^2−2
8x^2−x

Differentiate with respect to x:f(x)=(ax3+bx)

3ax2+b
ax^2+b
3x^2+1
3ax^2+x

Findf(x)=x^27

27x^26
x^26
26x^27
27x