Solve the following differential equation :

$$x \sin(y)dx+(x+1)\cos(y) dy$$

Here's where i'm stuck. I've let M=x siny and N=(x+1)cosy

Differentiating partially for both $M_y$=x cosy and $N_x$=cosy


I used a trick such that instead of x-1 I used x+1-2 and integrated to get my integrating factor as $e^x - \frac{1}{(x+1)^2}$

Now what do I do? I've tried multiplying my original equation by my integrating factor but it's long and disgusting and seems wrong. I have no idea how to proceed from here can anyone advise me

  • 1
    $\begingroup$ do you meant $$x\sin(y)dx+(x+1)\cos(y)dy=0$$? $\endgroup$ – Dr. Sonnhard Graubner Mar 1 '18 at 17:03

if so then write your equation in the form $$\frac{x}{x+1}dx=-\frac{\cos(y)}{\sin(y)}dy$$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.