Answer in Differential Equations for Cypress #150976

Question #150976

If y(t)=c*e^(-2t)+t+1 is general solution to y'+p(t)*y=g(t), then p(t) and g(t)=?

Expert's answer

Let $y(t)=Ce^{-2t}+t+1$ be the general solution of $y'+p(t)y=g(t)$ .

Then $y'(t)=-2Ce^{-2t}+1$ . Taking into account that $y'(t)+2y(t)=-2Ce^{-2t}+1+2(Ce^{-2t}+t+1)=2t+3$ , we conclude that

$p(t)=2$ and $g(t)=2t+3.$

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Comments

Assignment Expert

16.12.20, 00:24

Dear Cypress, in this problem y'(t)=2y(t) is not a correct equation. The solution proves y'(t)+2y(t)=2t+3. The formula y(t)=c*exp(-2t)+t+1 was given in the question and by differentiating this formula with respect to t you can deduce y'(t)=-2c*exp(-2t)+1. Substituting the corresponding expressions for y(t), y'(t) into y'(t)+2y(t) and simplifying one gets y'(t)+2y(t)=2t+3.

Cypress

15.12.20, 16:06

How did you found y'(t)=2y(t)? I don't get that.