What is the solution for dy=x^2sin(8x)dx ?

The solution for dy=x^2sin(8x)dx is y=-1/8 x^2cos(8x)+1/256 (8xsin(8x)+cos(8x))+c_{1}

Popular >

dy=x^2sin(8x)dx

d y = x^{2} sin (8 x) d x

y = - \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x)) + c_{1}

Solution steps

d y = x^{2} sin (8 x) d x

Let

y

be the dependent variable. Divide by

d x

\frac{d y}{d x} = x^{2} sin (8 x)

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = x^{2} sin (8 x)

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int x^{2} sin (8 x) d x

\int x^{2} sin (8 x) d x = - \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x)) + c_{1}

y = - \frac{1}{8} x^{2} cos (8 x) + \frac{1}{256} (8 x sin (8 x) + cos (8 x)) + c_{1}

\frac{\partial}{\partial y} (x^{2} y^{3} sin (x - 2 y))

x \to 7 lim (x + 6)

y^{^{'}} = \frac{x}{14 y}

\int_{\frac{3 π}{2}}^{2 π} - 4 sin (x) d x

x \to - 2 lim (ln (x + 2))

What is the solution for dy=x^2sin(8x)dx ?
The solution for dy=x^2sin(8x)dx is y=-1/8 x^2cos(8x)+1/256 (8xsin(8x)+cos(8x))+c_{1}