Differential Equation Calculator

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Differential equations constitute an important section in Calculus. Differential equations are the equations which contain

derivatives of dependent and independent variables in them.There are many methods of solving differential equations and

differential equation calculator is the instant online tool very helpful in giving the solution to differential equations.

Example 1: Using the variable separation method, solve the given differential equation. dy =  (3x + 1)dx
y

In order to solve the given differential equation, cross-multiply ‘y’ to the other side.

ydy = (3x + 1)dx

Now integrate the above equation to get the solution.

∫y dy = ∫(3x + 1)dx

∫y dy = ∫3x dx + ∫1 dx

y2/2 = 3x2/2 + x + c, where ‘c’ is a constant.

Hence the general solution of the given differential equation is y2/2 = 3x2/2 + x + c

Example 2: Using the variable separation method, solve the given differential equation.

y3dy + x2 dx = 0

The above differential equation is already in the required form.

Now we integrate the given equation to get a solution.

∫y3dy + ∫x2 dx = ∫0

y4/4 + x3/3  = c, where ‘c’ is a constant.

Hence the general solution of the given differential equation is y4/4 + x3/3 = c