Tuesday, November 3, 2015

Advanced Math Solutions – Ordinary Differential Equations Calculator, Exact Differential Equations

In the previous posts, we have covered three types of ordinary differential equations, (ODE). We have now reached the last type of ODE. In this post, we will talk about exact differential equations.

What is an exact differential equation?

There must be a 0 on the right side of the equation and M(x,y)dx and N(x,y)dx must be separated by a +.

Steps to solve exact differential equations:
  1. Verify that \frac{∂M(x,y)}{∂y}=\frac{∂N(x,y)}{∂x}
    • Find M(x,y) and N(x,y)
  2. Integrate \int M(x,y)dx or \int N(x,y)dy
    • This will help us find Ψ(x,y)
  3. Replace c with ƞ(x) if you integrated N(x,y) with respect to y, or ƞ(y) if you integrated M(x,y) with respect to x
  4. Compute ƞ(x) or ƞ(y)
  5. Solve to get the implicit or explicit solution, depending on which is preferred
    • Don’t forget to substitute ƞ(x) or ƞ(y)

Exact differential equations can be tricky. We will solve the first example step by step to help you better understand how to solve exact differential equations.

First example (click here):

1. Verify that \frac{∂M(x,y)}{∂y}=\frac{∂N(x,y)}{∂x}

2. Integrate \int N(x,y)dy

3. Replace c with ƞ(x)

4. Compute ƞ(x)

We took the derivative with respect to x of Ψ(x,y), which is equal to y+x^2 y+y^2+ƞ(x). We then compared the derivative to M(x,y), the equation we didn’t integrate. We then integrated both sides to solve for ƞ(x).

5. Find the implicit equation

Here’s another example (click here):

Exact differential equations may look scary because of the odd looking symbols and multiple steps. If you double check your work, memorize the steps, and practice, you can definitely get this concept down. Don’t be afraid and dive in!

Until next time,



  1. Find the function u(u,t), define for 0<x<π and t≥0, which satisfies the following condition:
    du/dt=(d^2 u)/〖dx〗^2 u(θ,t)=u(π,t)=0

  2. Thanks. This is a good help to those students who afraid to differential equations. But I think that the way it can be memorized should be applications of differential equatons.

  3. This is really interesting but i need urgent solution to this questions
    1. solve d^2y/dx^2-4dy/dx+4y=8(x^2+e^2x)
    2. determine the regular singular point of the differential equation 2x(x-1)y"+3(x+1)y'-y=0

  4. This was really informative and valuable information. Visit for the creative Website Designing and Development Services by Ogen Info system.
    Top 5 Website Designing Company in India

  5. Visit for the best Logistics and Freight Forwarders Companies in Delhi at Y & H Cargo India.
    Logistics Company in Delhi

  6. Spin Gurus is provided you the best service of Music Production.
    Sound Engineering Courses

  7. Nice Blog. If you Need best Mutual Fund in India MutualFundWala is best for you.
    Mutual Fund Agent

  8. Good Job if You Travel to kashmir and Want To Get Best Saffron walnuts i Suggest Go to kashmir online shopping

  9. zederex
    high-sugar refined meals are pressure. Whenever individuals are overworked or under severe emotional or mental pressure, they seek relief in meals. This invariably leads to a vitamin surplus and excess bodyweight. Massage is known to help relax the ideas and the whole personal whole body and bring

  10. Joint FLX
    groups. The thinning locks is unexpected and exhibits itself in little, smooth-skinned places that are likely to progressively expand progressively. It also impacts the sufferer’s claws, giving them a rough, ridged or inadequate overall look. The actual cause is still unidentified, although current concepts include of an

  11. Keto fit pro
    . health and health andis, “what happened to my waistline?” But, what you may not know is that studies suggest that our minds can sometimes be our biggest enemy when we are trying to get rid of fat. Our brains can actually hinder our systems from experiencing the burden decrease we desire. How? In today’s post I will discuss the

  12. cerisea medica gasping for breath. There are numerous techniques to manage fattiness. Dieting and training are the known measures but today health and fitness and health goods are becoming increasingly popular. Various organic and non-herbal weight-loss items have come in to market and so you have many choices throwing

  13. slim quick keto
    that have a high-content of frequent normal water and most may basically be recognized like some clean vegetables and fruits and clean vegetables but certain weight loss programs may limit meals with high-water content. In this case you will basically have to take more frequent normal water. Diuretics rmal water every ass of frequent normal water before

  14. It is very informative there is no doubt about it. I found this one pretty fascinating and it should go into my Collection. Very good work!
    office.com/setup | norton.com/setup | norton.com/setup