# Math Help - initial value problem DFQ

1. ## 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

2. 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?

3. 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: $\sin x \cdot y' + y\cos x = x\sin x \implies ( y\sin x ) ' = x\sin x$

4. ## Answer??

Is this the answer?? ..

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

5. 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 ????

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

y= (-2yln(sinx)-x^2)/2 + 4 - pi^2/4 ????
no. where did ln... come from?