# Thread: 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

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

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 $\displaystyle y \sin x$ (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

THANKS
Hint: $\displaystyle \sin x \cdot y' + y\cos x = x\sin x \implies ( y\sin x ) ' = x\sin x$

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 $\displaystyle y \sin x$ (by the product rule)

now can you continue?