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Differential Equation Calculator

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Differential equation is an equation of a function with its derivatives. Differential equation is expressed in the form of y = f(x), where y is the function of a variable x. The highest derivative present in the equation is the order of differential equation. Differential equation can be classified depending upon the order of derivative,
  • First order differential equation,
  • Second order differential equation,
  • Third order differential equation.
 

Steps

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Step 1 : Observe the problem and check whether it is in the form, y' = f(x).

Step 2 : Separate the x variable in one side and y variable on other side.

Step 3 : By integrating on both the sides, we will get differential equation.

Problems

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Given below are the problems for your references.

Solved Examples

Question 1:  Solve the differential equation :
$\frac{dy}{dx}$ = 7x - 3 ?

Solution:
 
Step 1 : Given, $\frac{dy}{dx}$ = 7x - 3

Step 2 : Separating both the variables,
dy = (7x - 3)dx

Step 3 : By integrating on both sides,
$\int dy = \int (7x - 3)dx$

      y = 7 $\int xdx - 3 \int dx$

     y = 7 $\frac{x^{2}}{2}$ - 3x

     y = $\frac{7x^{2}}{2}$ - 3x + c

Therefore, the differential equation of $\frac{dy}{dx}$ = 7x - 3 is y = $\frac{7x^{2}}{2}$ - 3x + c, where c is the arbitrary constant.
 

Question 2: Solve the differential equation :
$\frac{dy}{dx}$ = -x$e^{x}$ ?
Solution:
 
Step 1 : Given, $\frac{dy}{dx}$ = -x$e^{x}$

Step 2 : Separating both the variables,
$dy = -xe^{x}dx$

Step 3 : By integrating on both sides,
$\int dy = \int -xe^{x}dx$

      $y = - xe^{x} + \int e^{x}dx + c$

      $y = (1 - x)e^{x} + c$
     
Therefore, the differential equation of $\frac{dy}{dx}$ = -x$e^{x}$ is $y = (1 - x)e^{x} + c$, where c is the arbitrary constant.