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7 reasons why is differential equations so hard

Differential equations are one of the most difficult calculus subjects that students struggle with.

In this article, we’re going to discover the 7 crucial reasons Why students struggle or find Differential equations so hard.

1 – it requires solid basics in algebra 

The first thing that makes differential equations difficult for many students is, that it is a sequential subject meaning you have to build long years of experience studying algebra and high school by preparing a lot of other math topics to be final and eligible to study differential equations.

 The problem with students who struggle in differential equations is the gaps or knowledge holes they build up or expand over the years through missing or not understating foundational topics. 

In other words, they miss the basics they take in high school and also in college, especially algebra.

If you have weak foundations in an algebra course, especially on polynomials and functions you will struggle for sure in differential equations. Differential equations include a lot of different functions and techniques like solving equations and inequalities students should always be good at.

For instance, to solve a first differential equations degree you must have a solid foundation and good background to solve systems and matrices. 

You could read this article on linear algebra differential equations first.

2 – it requires solid basics in precalculus

The second reason that makes the students struggle in differential equations or find it hard is having week basics in pre-calculus. we find a lot of students who make mistakes about taking pre-calculus later in College. While they should study it in high school.

 simply because it’s better and more efficient to take it in high school than in college. you will find all the details reasons about this subject in this article.

Precalculus course is made to prepare students for difficult calculus courses in college like multivariable calculus and differential equations. in the pre-calculus course students Focus on the necessary topics, they will be needing for math College including:

 All these topics are essential for students to focus on and study hard. But unfortunately, it is not happening with almost all students.

 someones ignore the precalculus course while others skip it which causes dramatic consequences, failing in differential equations is the most frequent example.

3 – it requires solid basics in calculus

Another reason that makes students find hardships in differential equations is having weak basics in calculus courses. this problem has two outcomes:

If you belong to the first case, which is you’ve been studying hard calculus courses like calculus 1 or 2, and still find hardships to pass calculus 2. It’s probably that you didn’t study it or absorb the precalculus topics before, or give it much effort. As a result, lead to failing and suffering in differential equations.

This is the dark thing about differential equations. if you failed or struggled in pre-calculus you would struggle automatically in calculus then finally in differential equations. 

So it is like building a house that’s:

4 – need critical thinking 

Even if you do everything right by taking precalculus courses and calculus you’ll still need to be fighting in differential equations. That is obvious because it is the most difficult course in a bachelor’s or college. It is the last difficult subject you’ll be taking before taking your degree and applying for jobs.

 But it requires having strong critical thinking skills and diligence.

You will be using your critical thinking abilities to solve difficult equations that include derivatives, integrals, and trigonometry functions.

You don’t have to worry. you already have enough skills to study this subject. Especially if you succeed in the calculus 2 courses.

 if you haven’t yet taken calculus 2 courses we will not recommend taking differential equations it would be difficult even if your school allowed you to do that.

5 – need memorization

The Other unexpectable thing that students don’t take into account in differential equations is having some skills of memorization. 

For instance, in first and second-degree differential equations you will be required to memorize some homogeneous solutions.

But in general, it doesn’t require a lot of memorization like you might expect in biology or Humanity courses. just a few tricks and equations to memorize nothing else more.

6 – time and effort consuming

The other reason that makes some students suffer in differential equations is not giving enough time and effort. the differential equation is a topic that requires a lot of effort and time to spend if you want to absorb it.

 It is not a topic you’ll be acquiring or understanding like statistics by studying for 1 hour a day. is the subject that requires at least 3 hours a day of practice solving equations and learning tricks to get enough experience to finally succeed at the exams.

 so it is not intuitive at all it requires a lot of training and hard work. 

7 – it requires understanding some theories 

The last difficulty that students find in differential equations is understanding a few theorems they need to need to apply like the Euler theorem and Laplace transform.

differential equations are is a little bit difficult and require additional effort and patience to understand.

Conclusion

The differential equation is a difficult topic you cannot make it easier because actually not the case.  

But The only thing that increases your odds of success is to be good or have solid foundations in the previous calculus courses, especially calculus 2 and Calculus 1.