# Thread: Solving differential equations by inspection!

1. ## Solving differential equations by inspection!

I have this question 1. Solve the following DE’s, by inspection.
y’= -sin x

I Know that y=cos x and y'= -sin x. Then is y=cos x the answer? What does it mean when solve by inspection???

2. ## Re: Solving differential equations by inspection!

Solving by inspection involves exactly what you did (well, almost, you forgot the constant of integration)...you know that:

$\displaystyle \frac{dy}{dx}=\frac{d}{dx}(\cos(x)+C)=-\sin(x)$ and so we must have:

$\displaystyle y=\cos(x)+C$

3. ## Re: Solving differential equations by inspection!

Oh thanks for the reply!

Then let's say for y'' = 3 and I did. y'=3x+c
y= (3/2)x^2 +C

Then is y= (3/2)x^2 + C answer for y"=3?

Thank you.

4. ## Re: Solving differential equations by inspection!

No, for the second example, you should observe that:

$\displaystyle \frac{d^2}{dx^2}\left(\frac{3}{2}x^2+c_1x+c_2 \right)=3$ hence:

$\displaystyle y=\frac{3}{2}x^2+c_1x+c_2$

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### how to solve differential equations by inspection

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