# initial value problem DFQ

• Jan 16th 2009, 12:48 PM
cheertcc101
initial value problem DFQ
I need to solve this initial value problem:

sin(x)dy/dx + ycos(x) = xsin(x) with initial condition y(pi/2)=2

THANKS
• Jan 16th 2009, 12:52 PM
Jhevon
Quote:

Originally Posted by cheertcc101
I need to solve this initial value problem:

sin(x)dy/dx + ycos(x) = xsin(x) with initial condition y(pi/2)=2

THANKS

the book has these kinds of problems. it is just that here, the started you midway. does the "integrating factor method" ring a bell?

hint: note that the left hand side is the derivative of $y \sin x$ (by the product rule)

now can you continue?
• Jan 16th 2009, 12:58 PM
ThePerfectHacker
Quote:

Originally Posted by cheertcc101
I need to solve this initial value problem:

sin(x)dy/dx + ycos(x) = xsin(x) with initial condition y(pi/2)=2

THANKS

Hint: $\sin x \cdot y' + y\cos x = x\sin x \implies ( y\sin x ) ' = x\sin x$
• Jan 16th 2009, 01:08 PM
cheertcc101

y= (-2yln(sinx)-x^2)/2 + 4 - pi^2/4 ????
• Jan 16th 2009, 01:09 PM
cheertcc101
Quote:

Originally Posted by Jhevon
the book has these kinds of problems. it is just that here, the started you midway. does the "integrating factor method" ring a bell?

hint: note that the left hand side is the derivative of $y \sin x$ (by the product rule)

now can you continue?