Please Check This Sentence?

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Anyone have a suggestion or comment about my sentence, please leave your idea. Actually I want to change this sentence to be more easier to understand for reader.

"Ordinary differential equations play an extremly important and useful role in applied mathematics, engineering and physics. In most real world phenomena, the ordinary differential equation that model the problem usually in nonlinear differential equations that cannot be solved using analytic technique. Therefore, numerical methods are usually required."

thank you~
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Ordinary differential equations play a key role in applied mathematics, engineering and physics. In most real-world phenomena, ordinary differential equations usually model the problem in nonlinear differential equations that cannot be solved using analytic techniques, so numerical methods are usually required.

I don't understand what's going on, but I think I've got the sentence simplified.
May I add some sentence, for example:
Ordinary differential equations (ODEs) play a key role in applied mathematics, engineering and physics. In most real-world phenomena, ODEs usually model the problem in nonlinear differential equations that cannot be solved using analytic techniques. Hence, there is a need for methods that enable an efficient treatment of such problems. Therefore, numerical methods are ussually required in order to approximate the solution of ODEs.
I think this sentence is quite messy, may you give any idea to make this sentence easily understood ..thank you~
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I have a problem with this in terms of logic.

Are you saying that nonlinear differential equations are or are not the same as ordinary differential equations?

I don't think this is made clear. You seem to be saying that one kind of equation models problems by using another kind of equation. This doesn't make sense. It's like saying that dotted lines on a map represent territories by using solid lines. You can't have it both ways.

CJ
I have made some modification in my sentences and I think it might clear than the previous one. "Ordinary differential equations (ODEs) is a mathematical models that play a key role in modelling real-world problems. This application could be seen in physics, engineering, chemistry, biology and astronomy. The transformation of real-world problems into a mathematical equations are for analysing and giving a solutions via an appropriate techniques. In many applications, ODEs usually in the form of nonlinear differential equation that cannot be solved using analytic techniques. Hence, there is a need for methods that enable an efficient treatment of such problems. Therefore, numerical approximation techniques are a powerful tool giving the solutions we desired."
actually this is part of my thesis abstract.
I have underlined the grammar errors. I leave the examination of meaning to CJ:

Ordinary differential equations (ODEs) is a mathematical models that play a key role in modelling real-world problems. This application could be seen in physics, engineering, chemistry, biology and astronomy. The transformation of real-world problems into a mathematical equations are for analysing and giving a solutions via an appropriate techniques. In many applications, ODEs usually in the form of nonlinear differential equation that cannot be solved using analytic techniques. Hence, there is a need for methods that enable an efficient treatment of such problems. Therefore, numerical approximation techniques are a powerful tool giving the solutions we desired
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thanks a lot mister micawber! I hope CJ could give several idea in order to make this sentences free of mistakes and easily understood.
hye MM! this is my fully thesis abstract, I really hope you can check it..thank you~
myviOrdinary differential equations (ODEs) is a mathematical models that play a key role in modelling real-world problems. This application could be seen in physics, engineering, chemistry, biology and astronomy. The transformation of real-world problems into a mathematical equations are for analysing and giving a solutions via an appropriate techniques. In many applications, ODEs usually in the form of nonlinear differential equation that cannot be solved using analytic techniques. Hence, there is a need for methods that enable an efficient treatment of such problems. Therefore, numerical approximation techniques are a powerful tool giving the solutions we desired.
I think you just need to move things around a little and make a few changes. I tried to keep most of what you wrote.

Ordinary differential equations (ODEs) play a key role in modelling real-world problems such as are seen in physics, engineering, chemistry, biology, and astronomy. In many applications where real-world problems are transformed into mathematical equations, ODEs take the form of nonlinear differential equations that cannot be solved using analytic techniques. There is therefore a need for different methods for treating such problems efficiently and obtaining the desired solutions. Numerical approximation techniques are a powerful tool for meeting this need.

CJ
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