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# Differential equations Calculator

## Get detailed solutions to your math problems with our Differential equations step by step calculator. Sharpen your math skills and learn step by step with our math solver. Check out more online calculators here.

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### Difficult Problems

1

Solved example of Separable differential equations

$\frac{dy}{dx}=y-x\cdot y$
2

Multiply both sides of the equation by $dx$

$dy=\left(y-xy\right)dx$
3

Factoring by $y$

$dy=y\left(1-x\right)dx$
4

Integrate both sides, the left side with respect to $y$, and the right side with respect to $x$

$\int1dy=\int\left(1-x\right)dx$
5

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int1dy=\int1dx+\int-xdx$
6

The integral of a constant is equal to the constant times the integral's variable

$y=\int1dx+\int-xdx$
7

The integral of a constant is equal to the constant times the integral's variable

$y=x+\int-xdx$
8

Take the constant out of the integral

$y=x-\int xdx$
9

Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

$y=x-\frac{1}{2}x^2$
10

As the integral that we are solving is an indefinite integral, when we finish we must add the constant of integration

$y=x-\frac{1}{2}x^2+C_0$

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