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Separable differential equations Calculator

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1

Example

$\left(2x-1\right)\cdot dx+\left(3y+7\right)\cdot dy=0$
2

Grouping the terms of the differential equation

$\left(7+3y\right)dy=-\left(2x-1\right)dx$
3

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

$\int\left(7+3y\right)dy=\int-\left(2x-1\right)dx$
4

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

$\int7dy+\int3ydy=\int-\left(2x-1\right)dx$
5

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

$7y+\int3ydy=\int-\left(2x-1\right)dx$
6

Take the constant out of the integral

$7y+\int3ydy=-\int\left(2x-1\right)dx$
7

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

$7y+\int3ydy=-\left(\int-1dx+\int2xdx\right)$
8

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

$7y+\int3ydy=-\left(\int2xdx-x\right)$
9

Take the constant out of the integral

$7y+\int3ydy=-\left(2\int xdx-x\right)$
10

Take the constant out of the integral

$7y+3\int ydy=-\left(2\int xdx-x\right)$
11

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

$7y+3\int ydy=-\left(2\cdot \frac{1}{2}x^2-x\right)$
12

Multiply $\frac{1}{2}$ times $2$

$7y+3\int ydy=-\left(1x^2-x\right)$
13

Any expression multiplied by $1$ is equal to itself

$7y+3\int ydy=-\left(x^2-x\right)$
14

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

$7y+3\cdot \frac{1}{2}y^2=-\left(x^2-x\right)$
15

Multiply $\frac{1}{2}$ times $3$

$7y+\frac{3}{2}y^2=-\left(x^2-x\right)$
16

Rewrite the equation

$7y+\frac{3}{2}y^2-x+x^2=0$
17

Factoring by $y$

$-x+x^2+y\left(7+\frac{3}{2}y\right)=0$
18

Add the constant of integration

$-x+x^2+y\left(7+\frac{3}{2}y\right)=0+C_0$