# Solving differential equations by inspection!

• November 11th 2012, 09:39 PM
tjsdndnjs
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???
• November 11th 2012, 09:49 PM
MarkFL
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:

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

$y=\cos(x)+C$
• November 11th 2012, 09:55 PM
tjsdndnjs
Re: Solving differential equations by inspection!

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.
• November 11th 2012, 10:06 PM
MarkFL
Re: Solving differential equations by inspection!
No, for the second example, you should observe that:

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

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