## Related questions with answers

Question

Graph several functions that satisfy the following differential equations. Then find and graph the particular function that satisfies the given initial condition. f'(x)=2x-5; f(0)=4

Solution

VerifiedAnswered 6 months ago

Answered 6 months ago

Step 1

1 of 2A function $F$ is and antiderivative of $f$ on an interval $I$ provided $F'(x)=f(x)$, for all $x$ in $I$.

$\begin{align*} F(x)&=\int 2x-5 \, dx \\ &= \int 2x \, dx-\int 5 \, dx\\ &=x^2-5x+C \end{align*}$

We are given that $F(0)=4$, therefore

$\begin{gather*} F(0)=4\\ 0^2-5(0)+C=4\\ \boxed{C=4} \end{gather*}$

Therefore,

$\begin{gather*} F(x)=x^2-5x+4 \end{gather*}$

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