# differential equation

#### Timson28

##### New member
I solved this differential equation but I'm not sure if I'm right.

Would you check it?

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#### Zermelo

##### New member
Try to plug the solution in the original equation, the same way you would verify solutions of a “normal” (for example linear) equation, see what will you get.

#### HallsofIvy

##### Elite Member
First note that $$\displaystyle e^{a+ b}= e^ae^b$$ so you can write your solution as
$$\displaystyle y= e^{c_1}e^{-x}- 1$$.

And, since $$\displaystyle c_1$$ is an arbitrary constant, so is $$\displaystyle e^{c_1}$$ so let $$\displaystyle C= e^{c_1}$$ and
$$\displaystyle y= Ce^{-x}- 1$$.

Now, $$\displaystyle y'= -Ce^{-x}$$ so what is $$\displaystyle y'+ xy+ x$$?

#### skeeter

##### Elite Member
$$\displaystyle \frac{dy}{dx} = -x(y+1)$$

$$\displaystyle \frac{dy}{y+1} = -x \, dx$$

now integrate …

#### Timson28

##### New member
omg i see my foult. Thx

#### Subhotosh Khan

##### Super Moderator
Staff member
I solved this differential equation but I'm not sure if I'm right.

Would you check it?

Differentiate the function you derived and see whether that satisfies the given DE.​

• Jomo

#### Jomo

##### Elite Member
I solved this differential equation but I'm not sure if I'm right.

Would you check it?