initial value problem DFQ

• January 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

Please help there are NO examples of my book of this type of problem

THANKS
• January 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

Please help there are NO examples of my book of this type of problem

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?
• January 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

Please help there are NO examples of my book of this type of problem

THANKS

Hint: $\sin x \cdot y' + y\cos x = x\sin x \implies ( y\sin x ) ' = x\sin x$
• January 16th 2009, 01:08 PM
cheertcc101
Is this the answer?? ..

y= (-2yln(sinx)-x^2)/2 + 4 - pi^2/4 ????
• January 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?

Is this the answer?? ..

y= (-2yln(sinx)-x^2)/2 + 4 - pi^2/4 ????
• January 16th 2009, 01:49 PM
Jhevon
Quote:

Originally Posted by cheertcc101
Is this the answer?? ..

y= (-2yln(sinx)-x^2)/2 + 4 - pi^2/4 ????

no. where did ln... come from?