# How to solve this very hard nonlinear ordinary differential equation: $4y^{3}+7x\sin(x)+4x^{4}-(16\cos(y)-7x-\frac{7}{4}y^{2})y'=-e^{y-x}+\sinh(y)$

$$4\cdot y^{3}+7\cdot x\cdot\sin(x)+4\cdot x^{4}-\left(16\cdot\cos(y)-7\cdot x-\frac{7}{4}\cdot y^{2}\right)\cdot y'=-e^{y-x}+\sinh(y)$$

I tried a lot to solve this differential equation. I think it must have a strange integrator factor.

• 1. Please write formulas in MathJax.  2. Please show us your attempts to solve this task so that we can really help you. Oct 24, 2022 at 22:12
• Since you tried "a lot", please include your attempts to solve this. Oct 24, 2022 at 22:14
• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Oct 24, 2022 at 22:15
• May I ask what is the origin of this rather bizarre equation? Oct 24, 2022 at 23:43
• This nonlinear first order differential equation was a score question of Amir Kabir University of Iran. There were 7 questions and I solved 6 of them. This question is not complete. I think it can be solved by finding an integrator Oct 25, 2022 at 0:51